Question

计算(x+2)(x-6)+16;(x-y)^2+4xy;2a(x^2+1)^2-2ax^2;25(a+b)^2-9(a-b)^2;(a+3b)^2-10(a+3b)+25

因式分解，要写过程

Answer 1

(x+2)(x-6)+16
=x^2-4x-12+16
=x^2-4x+4
=(x-2)^2

(x-y)^2+4xy
=x^2+y^2-2xy+4xy
=x^2+y^2+2xy
=(x+y)^2

2a(x^2+1)^2-2ax^2
=2a[(x^2+1)^2-x^2]
=2a(x^2+1-x)(x^2+1+x)

25(a+b)^2-9(a-b)^2
=[5(a+b)-3(a-b)][5(a+b)+3(a-b)]
=(5a+5b-3a+3b)(5a+5b+3a-3b)
=(2a+8b)(8a+2b)
=4(a+4b)(4a+b)

(a+3b)^2-10(a+3b)+25
=(a+3b-5)^2

Answer 2

(x+2)(x-6)+16=x^2-4x+4;
(x-y)^2+4xy=(x+y)^2;
2a(x^2+1)^2-2ax^2=2a(x^4+x^2+1);
25(a+b)^2-9(a-b)^2=;16a^2+16b^2+68ab
(a+3b)^2-10(a+3b)+25=(a+3b-5)^2

Answer 3

(x+2)(x-6)+16=x^2-4x+4=(x-2)^2
(x-y)^2+4xy=(x+2)^2
2a(x^2+1)^2-2ax^2=2a[(x^2+1)^2-x^2]=2a(x^+x+1)(x^2-x+1)
25(a+b)^2-9(a-b)^2=[5(a+b)]^2-[3(a-b)]^2=(5a+5b+3a-3b)(5a+5b-3a+3b)=4(4a+b)(4b+a)
(a+3b)^2-10(a+3b)+25=(a+3b-5)^2