618:
The known values assigned to the unlike part of two or more terms are called coefficients. As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both
243:
In this discussion, a "term" will refer to a string of numbers being multiplied or divided (that division is simply multiplication by a reciprocal) together. Terms are within the same expression and are combined by either addition or subtraction. For example, take the expression:
1043:
The expression is considered simplified when all like terms have been combined, and all terms present are unlike. In this case, all terms now have different unknown factors, and are thus unlike, and so the expression is completely simplified.
981:. By the rule in the first example, all terms with the same set of unknown factors, that is, all like terms, may be combined by adding or subtracting their coefficients, while maintaining the unknown factors. Thus, the expression becomes
770:
The first step to grouping like terms in this expression is to get rid of the parentheses. Do this by distributing (multiplying) each number in front of a set of parentheses to each term in that set of parentheses:
766:
892:
65:
More generally, when some variable are considered as parameters, like terms are defined similarly, but "numerical factors" must be replaced by "factors depending only on the parameters".
365:. and juxtapose that new number with the remaining unknown number. Terms combined in an expression with a common, unknown factor (or multiple unknown factors) are called like terms.
1039:
339:
If the expression in parentheses may be calculated, that is, if the variables in the expression in the parentheses are known numbers, then it is simpler to write the calculation
233:
123:
614:
927:
896:
The like terms in this expression are the terms that can be grouped together by having exactly the same set of unknown factors. Here, the sets of unknown factors are
956:
541:
335:
502:
276:
468:
442:
363:
979:
568:
416:
396:
298:
166:
146:
632:
1092:
776:
172:
of the equation and may be considered as parameters. Then, expanding the above product and regrouping the like terms gives
280:
There are two terms in this expression. Notice that the two terms have a common factor, that is, both terms have an
46:
that differ only by a numerical factor. Like terms can be regrouped by adding their coefficients. Typically, in a
619:
terms. Such combination is called combining like terms, and it is an important tool used for solving equations.
51:
986:
47:
178:
169:
78:
69:
578:
899:
1097:
1061:
931:
511:
305:
475:
249:
447:
421:
418:
have numerical values, so that their sum may be calculated. For ease of calculation, let
342:
961:
550:
401:
381:
283:
151:
131:
55:
1086:
17:
59:
31:
300:. This means that the common factor variable can be factored out, resulting in
43:
39:
761:{\displaystyle 3(4x^{2}y-6y)+7x^{2}y-3y^{2}+2(8y-4y^{2}-4x^{2}y)}
887:{\displaystyle 12x^{2}y-18y+7x^{2}y-3y^{2}+16y-8y^{2}-8x^{2}y}
27:
Terms that have the same variables and powers (in
Algebra)
989:
964:
934:
902:
779:
635:
581:
553:
514:
478:
450:
424:
404:
384:
345:
308:
286:
252:
181:
154:
134:
81:
1033:
973:
950:
921:
886:
760:
608:
562:
535:
496:
462:
436:
410:
390:
357:
329:
292:
270:
227:
160:
140:
117:
627:Take the expression, which is to be simplified:
50:, like terms are those that contain the same
8:
1025:
997:
988:
963:
939:
933:
907:
901:
875:
859:
834:
815:
787:
778:
746:
730:
699:
680:
649:
634:
580:
552:
513:
477:
449:
423:
403:
383:
344:
307:
285:
251:
186:
180:
153:
133:
80:
1053:
72:, one considers often the expression
378:To provide an example for above, let
7:
1034:{\displaystyle 11x^{2}y-2y-11y^{2}}
470:. The original expression becomes
25:
228:{\displaystyle x^{2}-(r+s)x+rs.}
68:For example, when considering a
755:
711:
667:
639:
527:
515:
321:
309:
207:
195:
109:
97:
94:
82:
1:
506:which may be factored into
118:{\displaystyle (x-r)(x-s),}
1114:
58:, possibly with different
623:Simplifying an expression
1093:Mathematical terminology
609:{\displaystyle 5x+3x=8x}
922:{\displaystyle x^{2}y,}
573:This demonstrates that
1035:
975:
952:
951:{\displaystyle y^{2},}
923:
888:
762:
610:
564:
537:
536:{\displaystyle (5+3)x}
498:
464:
438:
412:
392:
359:
331:
330:{\displaystyle (a+b)x}
294:
272:
229:
162:
142:
119:
1062:"Like terms in Depth"
1036:
976:
953:
924:
889:
763:
611:
565:
538:
499:
497:{\displaystyle 5x+3x}
465:
439:
413:
393:
360:
332:
295:
273:
271:{\displaystyle ax+bx}
230:
163:
143:
120:
48:polynomial expression
987:
962:
932:
900:
777:
633:
579:
551:
512:
476:
448:
422:
402:
382:
343:
306:
284:
250:
179:
152:
132:
79:
18:Combining like terms
463:{\displaystyle b=3}
437:{\displaystyle a=5}
358:{\displaystyle a+b}
1031:
974:{\displaystyle y.}
971:
948:
919:
884:
758:
606:
563:{\displaystyle 8x}
560:
533:
494:
460:
434:
408:
388:
355:
327:
290:
268:
225:
158:
138:
115:
70:quadratic equation
411:{\displaystyle b}
391:{\displaystyle a}
293:{\displaystyle x}
161:{\displaystyle s}
141:{\displaystyle r}
16:(Redirected from
1105:
1077:
1076:
1074:
1073:
1058:
1040:
1038:
1037:
1032:
1030:
1029:
1002:
1001:
980:
978:
977:
972:
957:
955:
954:
949:
944:
943:
928:
926:
925:
920:
912:
911:
893:
891:
890:
885:
880:
879:
864:
863:
839:
838:
820:
819:
792:
791:
767:
765:
764:
759:
751:
750:
735:
734:
704:
703:
685:
684:
654:
653:
615:
613:
612:
607:
569:
567:
566:
561:
542:
540:
539:
534:
503:
501:
500:
495:
469:
467:
466:
461:
443:
441:
440:
435:
417:
415:
414:
409:
397:
395:
394:
389:
364:
362:
361:
356:
336:
334:
333:
328:
299:
297:
296:
291:
277:
275:
274:
269:
234:
232:
231:
226:
191:
190:
167:
165:
164:
159:
147:
145:
144:
139:
124:
122:
121:
116:
21:
1113:
1112:
1108:
1107:
1106:
1104:
1103:
1102:
1083:
1082:
1081:
1080:
1071:
1069:
1060:
1059:
1055:
1050:
1021:
993:
985:
984:
960:
959:
935:
930:
929:
903:
898:
897:
871:
855:
830:
811:
783:
775:
774:
742:
726:
695:
676:
645:
631:
630:
625:
577:
576:
549:
548:
510:
509:
474:
473:
446:
445:
420:
419:
400:
399:
380:
379:
376:
371:
341:
340:
304:
303:
282:
281:
248:
247:
241:
182:
177:
176:
150:
149:
130:
129:
77:
76:
28:
23:
22:
15:
12:
11:
5:
1111:
1109:
1101:
1100:
1095:
1085:
1084:
1079:
1078:
1052:
1051:
1049:
1046:
1028:
1024:
1020:
1017:
1014:
1011:
1008:
1005:
1000:
996:
992:
970:
967:
947:
942:
938:
918:
915:
910:
906:
883:
878:
874:
870:
867:
862:
858:
854:
851:
848:
845:
842:
837:
833:
829:
826:
823:
818:
814:
810:
807:
804:
801:
798:
795:
790:
786:
782:
757:
754:
749:
745:
741:
738:
733:
729:
725:
722:
719:
716:
713:
710:
707:
702:
698:
694:
691:
688:
683:
679:
675:
672:
669:
666:
663:
660:
657:
652:
648:
644:
641:
638:
624:
621:
605:
602:
599:
596:
593:
590:
587:
584:
559:
556:
532:
529:
526:
523:
520:
517:
493:
490:
487:
484:
481:
459:
456:
453:
433:
430:
427:
407:
387:
375:
372:
370:
367:
354:
351:
348:
326:
323:
320:
317:
314:
311:
289:
267:
264:
261:
258:
255:
240:
239:Generalization
237:
236:
235:
224:
221:
218:
215:
212:
209:
206:
203:
200:
197:
194:
189:
185:
157:
137:
126:
125:
114:
111:
108:
105:
102:
99:
96:
93:
90:
87:
84:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1110:
1099:
1096:
1094:
1091:
1090:
1088:
1068:. Math Online
1067:
1063:
1057:
1054:
1047:
1045:
1041:
1026:
1022:
1018:
1015:
1012:
1009:
1006:
1003:
998:
994:
990:
982:
968:
965:
945:
940:
936:
916:
913:
908:
904:
894:
881:
876:
872:
868:
865:
860:
856:
852:
849:
846:
843:
840:
835:
831:
827:
824:
821:
816:
812:
808:
805:
802:
799:
796:
793:
788:
784:
780:
772:
768:
752:
747:
743:
739:
736:
731:
727:
723:
720:
717:
714:
708:
705:
700:
696:
692:
689:
686:
681:
677:
673:
670:
664:
661:
658:
655:
650:
646:
642:
636:
628:
622:
620:
616:
603:
600:
597:
594:
591:
588:
585:
582:
574:
571:
557:
554:
546:
545:or, equally,
543:
530:
524:
521:
518:
507:
504:
491:
488:
485:
482:
479:
471:
457:
454:
451:
431:
428:
425:
405:
385:
373:
368:
366:
352:
349:
346:
337:
324:
318:
315:
312:
301:
287:
278:
265:
262:
259:
256:
253:
245:
238:
222:
219:
216:
213:
210:
204:
201:
198:
192:
187:
183:
175:
174:
173:
171:
155:
135:
112:
106:
103:
100:
91:
88:
85:
75:
74:
73:
71:
66:
63:
61:
57:
53:
49:
45:
41:
37:
33:
19:
1070:. Retrieved
1065:
1056:
1042:
983:
895:
773:
769:
629:
626:
617:
575:
572:
547:
544:
508:
505:
472:
377:
338:
302:
279:
246:
242:
127:
67:
64:
60:coefficients
54:to the same
35:
29:
1066:Math Online
32:mathematics
1087:Categories
1072:2008-09-07
36:like terms
1048:Footnotes
1016:−
1007:−
866:−
850:−
825:−
797:−
737:−
721:−
690:−
659:−
193:−
104:−
89:−
52:variables
369:Examples
168:are the
40:summands
1098:Algebra
374:Example
128:where
56:powers
170:roots
42:in a
958:and
444:and
398:and
148:and
38:are
44:sum
30:In
1089::
1064:.
1019:11
991:11
844:16
800:18
781:12
570:.
62:.
34:,
1075:.
1027:2
1023:y
1013:y
1010:2
1004:y
999:2
995:x
969:.
966:y
946:,
941:2
937:y
917:,
914:y
909:2
905:x
882:y
877:2
873:x
869:8
861:2
857:y
853:8
847:y
841:+
836:2
832:y
828:3
822:y
817:2
813:x
809:7
806:+
803:y
794:y
789:2
785:x
756:)
753:y
748:2
744:x
740:4
732:2
728:y
724:4
718:y
715:8
712:(
709:2
706:+
701:2
697:y
693:3
687:y
682:2
678:x
674:7
671:+
668:)
665:y
662:6
656:y
651:2
647:x
643:4
640:(
637:3
604:x
601:8
598:=
595:x
592:3
589:+
586:x
583:5
558:x
555:8
531:x
528:)
525:3
522:+
519:5
516:(
492:x
489:3
486:+
483:x
480:5
458:3
455:=
452:b
432:5
429:=
426:a
406:b
386:a
353:b
350:+
347:a
325:x
322:)
319:b
316:+
313:a
310:(
288:x
266:x
263:b
260:+
257:x
254:a
223:.
220:s
217:r
214:+
211:x
208:)
205:s
202:+
199:r
196:(
188:2
184:x
156:s
136:r
113:,
110:)
107:s
101:x
98:(
95:)
92:r
86:x
83:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.