Question

化简下列各题 急

(1) (x-y)(x+y)-(x-2y)(2x+y)
(2) (1-4y)(1+4y)+(1+4y)^2
(3) (3x+5)^2-(3x-5)(3x+5)
(4) (2a-3b)^2(2a+3b)^2
计算：
(1) (-a+b+c)(a+b-c)
(2) (x-1)^2(x+1)^2(x^2+1)^2

Answer 1

你好：

(1) (x-y)(x+y)-(x-2y)(2x+y)
=x^2-y^2-(2x^2+xy-4xy-2y^2)
=x^2-y^2-2x^2+3xy+2y^2
=y^2+3xy-x^2

(2) (1-4y)(1+4y)+(1+4y)^2
=(1+4y)*[(1-4y)+(1+4y)]
=(1+4y)*2
=2+8y

(3) (3x+5)^2-(3x-5)(3x+5)
=(3x+5)*{(3x+5)-(3x-5)}
=(3x+5)*10
=15+30x

(4) (2a-3b)^2(2a+3b)^2
=[(2a-3b)(2a+3b)]^2
=(4a^2-9b^2)^2
=16a^4+81b^4-72a^2b^2

计算：
(1) (-a+b+c)(a+b-c)
=[b+(c-a)]*[b-(c-a)]
=b^2-(c-a)^2
=b^2-c^2-a^2+2ac

(2) (x-1)^2(x+1)^2(x^2+1)^2
=[(x-1)(x+1)]^2*(x^2+1)^2
=(x^2-1)^2*(x^2+1)^2
=[(x^2-1)*(x^2+1)]^2
=(x^4-1)^2
=x^8-2x^4+1

希望对你有帮助！