Đáp án:
1. (a+3b+1)(a+3b-1)
2. (2x-5).(-2)
3. (x+5)(x-3)
4. $(x+y)[(x+y)^2-1]$
5. (x-3)(x-2)(x+2)
6. (x-5y)(x-2y)
7. $(a^2-2)(a^2+2)$
Giải thích các bước giải:
$1.a^2+6ab+9b^2-1=(a^2+2.a.3b+(3b)^2)-1\\
=(a+3b)^2-1=(a+3b+1)(a+3b-1)\\$
$2) 4x^2-25+(2x+7)(5-2x)=(2x)^2-5^2+(2x+7)(5-2x)\\
=(2x-5)(2x+5)-(2x+7)(2x-5)\\
=(2x-5)(2x+5-2x-7)=(2x-5).(-2)\\
3) x^2+2x-15= (x^2+2x+1)-16\\
=(x+1)^2-4^2=(x+1+4)(x+1-4)\\
=(x+5)(x-3)\\$
$4.x^3-x+3x^2y+3xy^2-y+y^3\\
=(x^3+3x^2y+3xy^2+y^3)-(x+y)\\
=(x+y)^3-(x+y)\\
=(x+y)[(x+y)^2-1]\\
5.x^3-3x^2-4x+12\\
=x^2(x-3)-4(x-3)\\
=(x-3)(x^2-4)\\
=(x-3)(x-2)(x+2)$
$6.x^2-7xy+10y^2= x^2-5xy-2xy+10y^2\\
= x(x-5y)-2y(x-5y)=(x-5y)(x-2y)\\
7.a^4-4=(a^2)^2-2^2=(a^2-2)(a^2+2)$