Question

利用乘法公式计算 （3a+2)^2-(2a-1)^2 （x-y）（x+y)-(2x-y)^2 [（x+2)(x-2)]^2 (a+3)(a-3)(a^2+9)

(3a+2)^2-(2a-1)^2
（x-y）（x+y)-(2x-y)^2
[（x+2)(x-2)]^2
(a+3)(a-3)(a^2+9)

Answer 1

(3a+2)^2-(2a-1)^2={(3a+2)+(2a-1)} * {(3a+2)-(2a-1)}=(5a+1)(a+1)=5a*a+6a+1.
（x-y）（x+y)-(2x-y)^2 =xx-yy-4xx+4xy-4=-3x²+4xy-y²-4.
[（x+2)(x-2)]^2=(x²－4)²＝x^4－8x²＋16.
(a+3)(a-3)(a^2+9)=(a²－9)(a²＋9)＝a^4-81.

Answer 2

(1)5a^2+16a+3
(2)-3x^2-2y^2+4xy
(3)x^4-8x^2-16
(4)a^4-81

追问

过程

追答

(1)=9a^2+12a+4-4a^2+4a-1
=5a^2+16a+3
(2)=x^2-y^2-4x^2+4xy-y^2
=-3x^2-2y^2+4xy
（3）=(x^2-4)^2
=(x^2)^2-8x^2-16
=x^4-8x^2-16
(4)=(a^2-9)(a^2+9)
=a^4-81