Math, asked by KasishPilan2017, 1 year ago

Factorise
${a}^{12} {y}^{4} - {a}^{4} {y}^{12}$

Answers

Answered by adianshu1

Find the Greatest Common Factor (GCF)

How?

GCF=a4y4GCF={a}^{4}{y}^{4}GCF=a4y4

2

Factor out the GCF (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

a4y4(a12y4a4y4+−a4y12a4y4){a}^{4}{y}^{4}(\frac{{a}^{12}{y}^{4}}{{a}^{4}{y}^{4}}+\frac{-{a}^{4}{y}^{12}}{{a}^{4}{y}^{4}})a4y4(a4y4a12y4+a4y4−a4y12)

3

Simplify each term in parentheses

a4y4(a8−y8){a}^{4}{y}^{4}({a}^{8}-{y}^{8})a4y4(a8−y8)

4

Rewrite a8−y8{a}^{8}-{y}^{8}a8−y8 in the form a2−b2{a}^{2}-{b}^{2}a2−b2, where a=a4a={a}^{4}a=a4 and b=y4b={y}^{4}b=y4

a4y4((a4)2−(y4)2){a}^{4}{y}^{4}({({a}^{4})}^{2}-{({y}^{4})}^{2})a4y4((a4)2−(y4)2)

5

Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b)a2−b2=(a+b)(a−b)

a4y4(a4+y4)(a4−y4){a}^{4}{y}^{4}({a}^{4}+{y}^{4})({a}^{4}-{y}^{4})a4y4(a4+y4)(a4−y4)

6

Rewrite a4−y4{a}^{4}-{y}^{4}a4−y4 in the form a2−b2{a}^{2}-{b}^{2}a2−b2, where a=a2a={a}^{2}a=a2 and b=y2b={y}^{2}b=y2

a4y4(a4+y4)((a2)2−(y2)2){a}^{4}{y}^{4}({a}^{4}+{y}^{4})({({a}^{2})}^{2}-{({y}^{2})}^{2})a4y4(a4+y4)((a2)2−(y2)2)

7

Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b)a2−b2=(a+b)(a−b)

a4y4(a4+y4)(a2+y2)(a2−y2){a}^{4}{y}^{4}({a}^{4}+{y}^{4})({a}^{2}+{y}^{2})({a}^{2}-{y}^{2})a4y4(a4+y4)(a2+y2)(a2−y2)

8

Use Difference of Squares: a2−b2=(a+b)(a−b){a}^{2}-{b}^{2}=(a+b)(a-b)a2−b2=(a+b)(a−b)

a4y4(a4+y4)(a2+y2)(a+y)(a−y){a}^{4}{y}^{4}({a}^{4}+{y}^{4})({a}^{2}+{y}^{2})(a+y)(a-y)a4y4(a4+y4)(a2+y2)(a+y)(a−y)

KasishPilan2017: thanx

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