Question

因式分解：① (x+y)^2-(3x-2y)^2 ②9(2a+3b)^2-25(3a-b)^2 ③a^3+4a^2b+4ab^2 （每道题要过程，谢谢）

Answer 1

①(x+y)²-(3x-2y)²
=[(x+y)+(3x-2y)][(x+y)-(3x-2y)]
=(4x-y)(-2x+3y)

②9(2a+3b)²-25(3a-b)²
=[3(2a+3b)+5(3a-b)][3(2a+3b)-5(3a-b)]
=(21a+4b)(-9a+14b)

③a³+4a²b+4ab²
=a(a²+4ab+4b²)
=a(a+2b)²

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Answer 2

① (x+y)^2-(3x-2y)^2
=x^2+2xy+y^2-(9x^2-12xy+4y^2)
=-8x^2+14xy-3y^2
=-(8x^2-14xy+3y^2)
=-(2x-3y)(4x-y)

②9(2a+3b)^2-25(3a-b)^2
=9(4a^2+12ab+9b^2)-25(9a^2-6ab+b^2)
=36a^2+108ab+81b^2-225a^2+150ab-25b^2
=-189a^2+258ab+56b^2
=-(189a^2-258ab-56b^2)

=-(9a-14b)(21a+4b)

③a^3+4a^2b+4ab^2
=a*(a^2+4ab+4b^2)
=a*(a+2b)^2
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Answer 3

1、
原式=[(x+y)-(3x-2y)]*[(x+y)+(3x-2y)]=(3y-2x)(4x-y)

2、
原式=[3(2a+3b)-5(3a-b)]*[3(2a+3b)+5(3a-b)]=(14b-9a)(21a+4b)

3、
原式=a(a²+4ab+4b²)=a(a+2b)²

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Answer 4

a^3-4a^2b+4ab^2 =a(a^2-4ab+4b^2)=a(a-2b)^2 2:4y^2-(2z-x)^2=(2y+2z-x)(2y-2z+x) 3.:4x^2-y^2