Đáp án:
a/ x³+64
=x³+4³
=(x+4)(x²+4x+16)
b/ 9(x+5)²-(x-7)²
=[3(x+5)]²-(x-7)²
=[3(x+5)-(x-7)][3(x+5)+(x-7)]
=(3x+15-x+7)(3x+15+x-7)
=(2x+22)(4x+8)
=8(x+11)(x+2)
c/ x²-y²-x+y
=( x²-y²)-(x-y)
=(x-y)(x+y)-(x-y)
=(x-y)(x+y-1)
d/ (x+1)(x+2)(x+3)(x+4)-24
= [(x+1)(x+4)][(x+2)(x+3)] -24
=(x²+5x+4)(x²+5x+6)-24
+Đặt x²+5x+4=a, ta được :
a(a+2)-24
=a²+2a-24
=(a²+2a+1)-25
=(a+1)²-5²
=(a+1-5)(a+1+5)
=(a-4)(a+6)
⇔ (x²+5x+4-4)(x²+5x+4+6)
=x(x+5)(x²+5x+10)
e/ `81x^4` +4
= (`81x^4`+36x²+4)-36x²
=(9x²+2)²-(6x)²
=(9x²+2-6x)(9x²+2+6x)
f/ (x-y)²+4(x-y)-12
= [(x-y)²+4(x-y)+4] -16
=[(x-y)+2]²-4²
=(x-y+2-4)(x-y+2+4)
=(x-y-2)(x-y+6)
g/ `x^5`+`x^4`+1
= `x^5`+`x^4`+x²-x²+1
=`x^5`+`x^4`+x²-x²+1
=(`x^5`-x²)+(`x^4`+x²+1)
=x²(x²-1)+[(`x^4`+2x²+1)-x²]
=x²(x-1)(x²+x+1)+[(x²+1)²-x²]
=x²(x-1)(x²+x+1)+(x²+1-x)(x²+1+x)
=(x²+x+1)[x²(x-1)+(x²+1-x)]
=(x²+x+1)(x³-x²+x²+1-x)
=(x²+x+1)(x³+1-x)
h/ 4x²+4x-3
=(4x²+4x+1)-4
=(2x+1)²-2²
=(2x+1-2)(2x+1+2)
=(2x-1)(2x+3)
