Question

数学因式分解。

（5a+2b）^2=9b^2 ; 9x^2-y^2+4y-4 ;化简(a+b)(2a-2b)-2(a+2b)^2

Answer 1

(5a+2b)²-9b²=(5a+2b)-(3b)²
=(5a+2b+3b)(5a+2b-3b)
=(5a+5b)(5a-b)

(a+b)(2a-2b)-2(a+2b)²
=2(a+b)(a-b)-2(a²+4ab+4b²)
=2(a²-b²)-2a²-8ab-8b²
=-10b²-8ab.

Answer 2

（5a+2b）^2-9b^2 =(5a+2b+3b)(5a+2b-3b)=5(a+b)(5a-b)

9x^2-y^2+4y-4=9x^2-(y-2)^2=(3x+y-2)(3x-y+2)

(a+b)(2a-2b)-2(a+2b)^2=2(a^2-b^2)-2(a+2b)^2=2[a^2-b^2-(a+2b)^2]=-2(b^2+4ab+4b^2)=-2b(5b+4a)