Question

化简：（1）a^2-2(ab-b^2)-b^2 (2)(x^2-y^2)-3(2x^2-3y^2) (3)7a^b-(-4a^2b+5ab^2)-2(2a^b-3ab^2)

Answer 1

（1）a^2-2(ab-b^2)-b^2
=a^2-2ab+2b^2-b^2
=a^2-2ab+b^2

(2)(x^2-y^2)-3(2x^2-3y^2)
=x^2-y^2-6x^2+9y^2
=x^2-6x^2-y^2+9y^2
=-5x^2+8y^2

(3)7a^2b-(-4a^2b+5ab^2)-2(2a^2b-3ab^2)
=7a^2b+4a^2b-5ab^2-4a^2b+6ab^2
=7a^2b+4a^2b-4a^2b-5ab^2+6ab^2
=7a^2b+ab^2

Answer 2

解：1 原式=a^2-2ab+2b^2-b^2
=a^2-2ab+b^2
=(a-b)^2
解2 原式=x^2-y^2-6x^2+9y^2
=8y^2-5x^2
=(2√ 2y+√ 5x)(2√ 2y-√ 5x)

解3 原式＝7a^2b+4a^2b-5ab^2-4a^2b+6ab^2
=7a^2b+ab^2
=ab(7a+b)