因式分解81x^2-16y^2 9-(x+2)^2 -x^2+4 4(a+b)^2-(a-b)^2 x^4-x^2

题目

因式分解81x^2-16y^2 9-(x+2)^2 -x^2+4 4(a+b)^2-(a-b)^2 x^4-x^2
计算：10乘2^4+14 乘2^3+32 乘2^2

答案

81x^2-16y^2
=(9x-4y)(9x+4y)
9-(x+2)^2
=(3-x-2)(3+x+2)
=(1-x)(x+5)
-x^2+4
=4-x^2
=(2-x)(2+x)
4(a+b)^2-(a-b)^2
=[2(a+b)-(a-b)][2(a+b)+(a-b)]
=(2a+2b-a+b)(2a+2b+a-b)
=(a+3b)(3a+b)
x^4-x^2
=x^2(x^2-1)
=x^2(x+1)(x-1)
10*2^4+14*2^3+32*2^2
=10*2^4+7*2*2^3+8*2^2*2^2
=10*2^4+7*2^4+8*2^4
=2^4(10+7+8)
=2^4*25
=16*25
=400