\(a,\)

\(x^3y-y\)

\(=y\left(x^3-1\right)\)

\(=y\left[\left(x-1\right)\left(x^2+x+1\right)\right]\)

\(=y\left(x-1\right)\left(x^2+x+1\right)\)

\(b,\)

\(x^3y+y\)

\(=y\left(x^3+1\right)\)

\(=y\left[\left(x+1\right)\left(x^2-x+1\right)\right]\)

\(=y\left(x+1\right)\left(x^2-x+1\right)\)

\(c,\)

\(\left(x-y\right)^2-x\left(y-x\right)\)

\(=\left(x-y\right)^2+x\left(x-y\right)\)

\(=\left(x-y\right)\left(x-y+x\right)\)

\(=\left(x-y\right)\left(2x-y\right)\)

\(\left(x-y\right)^3-x^3+y^3=\left(x-y\right)^3-\left(x^3-y^3\right)=\left(x-y\right)^3-\left(x-y\right)\left(x^2+xy+y^2\right)=\left(x-y\right)\left(x^2-2xy+y^2-x^2-xy-y^2\right)=-3xy\left(x-y\right)\)

\(\left(x-y\right)^3-x^3+y^3\\ =\left(x-y\right)^3-\left(x^3-y^3\right)\\ =\left(x-y\right)^3-\left(x-y\right)\left(x^2+xy+y^2\right)\\ =\left(x-y\right)\left[\left(x-y\right)^2-\left(x^2+xy+y^2\right)\right]\\ =\left(x-y\right)\left(x^2-2xy+y^2-x^2-xy-y^2\right)\\ =\left(-3xy\right)\left(x-y\right)\)

\(\left(x-y\right)^3-x^3+y^3\)

\(=x^3-3x^2y+3xy^2-y^3-x^3+y^3\)

\(=-3x^2y+3xy^2\)

\(=-3xy\left(x-y\right)\)

\(\dfrac{xy}{2}-x+\dfrac{x^2}{4}=x\left(\dfrac{y}{2}-1+\dfrac{x}{4}\right)\)

\(x^2\left(x-3\right)^2-\left(x-3\right)^2-x^2+1=\left(x-3\right)^2\left(x^2-1\right)-\left(x^2-1\right)=\left(x^2-1\right)\left(x-3\right)^2=\left(x-1\right)\left(x+1\right)\left(x-3\right)^2\)

a) \(10x^2+10xy-x-y=10x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(10x-1\right)\)

\(-16a^4b^6-24a^5b^5-9a^6b^4\)

\(=-a^4b^4\left(16b^2+24ab+9a^2\right)\)

\(=-a^4b^4\left[\left(4b\right)^2+2\cdot4\cdot3\cdot ab+\left(3a\right)^2\right]\)

\(=-a^4b^4\cdot\left(3a+4b\right)^2\)

a) x³-2x²-x+2

=x(x²-1)+2(-x²+1)

=x(x²-1)-2(x²-1)

=(x²-1)(x-2)

b)

x²+6x-y²+9

=x²+6x+9-y²

=(x+3)²-y²

^{=(x+3-y)(x+3+y)}

A=x¹⁴+x⁷+1

   =(x¹⁴+x¹³+x¹²)-(x¹³+x¹²+x¹¹)+(x¹¹+x¹⁰+x⁹)-(x¹⁰+x⁹+x⁸)+(x⁸+x⁷+x⁶)-(x⁶+x⁵+x⁴)+(x⁵+x⁴+x³)-(x³⁺x²+x)+(x²+x+1)

Đặt B=x²+x+1

=>A=x¹²B-x¹¹B+x⁹B-x⁸B+x⁶B-x⁴B+x³B-xB+B

=>A=B(x¹²-x¹¹+x⁹-x⁸+x⁶-x⁴+x³-x+1)

Thay B=x²+x+1 vào A là xong

dùng bơ du là ra chư mấy

Do lười đánh máy nên tớ mới đặt B khi làm khỏi đặt cũng dc cái này là toán lớp 8

Lỗi?