Đáp án :
`a)A=(x^2+x-5)(x^2+x+3)`
`b)B=(x+y-4)(x+y+3)`
`c)C=(x^2+x+5)(x-1)(x+2)`
`d)D=(x+1)(x+6)(x^2+7x+16)`
Giải thích các bước giải:
`a)A=(x^2+x)^2-2(x^2+x)-15`
`Đặt a=x^2+x`
`<=>A=a^2-2a-15`
`<=>A=a^2-5a+3x-15`
`<=>A=a(a-5)+3(a-5)`
`<=>A=(a-5)(a+3)`
`<=>A=(x^2+x-5)(x^2+x+3)`
`b)B=x^2+2xy+y^2-x-y-12`
`<=>B=(x^2+2xy+y^2)-(x+y)-12`
`<=>B=(x+y)^2-(x+y)-12`
`Đặt a=x+y`
`<=>B=a^2-a-12`
`<=>B=a^2-4a+3a-12`
`<=>B=a(a-4)+3(a-4)`
`<=>B=(a-4)(a+3)`
`<=>B=(x+y-4)(x+y+3)`
`c)C=(x^2+x+1)(x^2+x+2)-12`
`Đặt x^2+x+1=a`
`<=>C=a(a+1)-12`
`<=>C=a^2+a-12`
`<=>C=a^2+4a-3a-12`
`<=>C=a(a+4)-3(a+4)`
`<=>C=(a+4)(a-3)`
`<=>C=(x^2+x+5)(x^2+x-2)`
`<=>C=(x^2+x+5)(x^2-x+2x-2)`
`<=>C=(x^2+x+5)[x(x-1)+2(x-1)]`
`<=>C=(x^2+x+5)(x-1)(x+2)`
`d)D=(x+2)(x+3)(x+4)(x+5)-24`
`<=>D=(x+2)(x+5)(x+3)(x+4)-24`
`<=>D=(x^2+7x+10)(x^2+7x+12)-24`
`Đặt x^2+7x+11=a`
`<=>D=(a-1)(a+1)-24`
`<=>D=a^2-1-24`
`<=>D=a^2-25`
`<=>D=(a-5)(a+5)`
`<=>D=(x^2+7x+6)(x^2+7x+16)`
`<=>D=(x^2+x+6x+6)(x^2+7x+16)`
`<=>D=[x(x+1)+6(x+1)](x^2+7x+16)`
`<=>D=(x+1)(x+6)(x^2+7x+16)`
Chúc bạn học tốt !!!
