Question

因式分解<1>81x^2-16y^2 <2>9-(x+2)^2 <3>-x^2+4 <4>4(a+b)^2-(a-b)^2 <5>x^4-x^2

计算：10乘2^4+14 乘2^3+32 乘2^2

Answer 1

<1>81x^2-16y^2
=(9x-4y)(9x+4y)

<2>9-(x+2)^2
=(3-x-2)(3+x+2)
=(1-x)(x+5)

<3>-x^2+4
=4-x^2
=(2-x)(2+x)

<4>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)

<5>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