a) x² ( x+ 2y) -x -2y

= x² ( x+ 2y) -(x+2y)

= (x²-1)(x+2y)

= (x-1)(x+1)(x+2y)

b)3x²- 3y² -2 (x-y)²

= 3(x²-y²) -2 (x-y)²

= 3(x-y)(x+y)-2(x-y)(x-y)

\(=\left(x-y\right)\left[3\left(x+y\right)-2\left(x-y\right)\right]\\ =\left(x-y\right)\left(3x+3y-2x+2y\right)\\ =\left(x-y\right)\left(x+5y\right)\)

c) x²- 2x-4y² - 4y

= (x²-4y²)-(2x+4y)

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

d) x³ - 4x² - 9x +36

= (x³+3x²)-(7x²+21x)+(12x+36)

= x²(x+3)-7x(x+3)+12(x+3)

=(x²-7x+12)(x+3)

\(=\left[\left(x^2-3x\right)-\left(4x-12\right)\right]\left(x+3\right)\\ =\left[x\left(x-3\right)-4\left(x-3\right)\right]\left(x+3\right)=\left(x-4\right)\left(x-3\right)\left(x+3\right)\)

cảm ơn bạn nhiều nha!

x³-5x²+2x+8

=x³-6x²+8x+x²-6x+8

=x(x²-6x+8)+(x²-6x+8)

=(x²-6x+8)(x+1)

=[x²-2x-4x+8](x+1)

=[x(x-2)-4(x-2)](x+1)

=(x-4)(x-2)(x+1)

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

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

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

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

------------------------------------

\(a^3+3a^2-6a-8\)

\(=a^3+4a^2-a^2-4a-2a-8\)

\(=\left(a^3+4a^2\right)-\left(a^2+4a\right)-\left(2a+8\right)\)

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

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

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

\(=\left(a+4\right)\left[\left(a^2-2a\right)+\left(a-2\right)\right]\)

\(=\left(a+4\right)\left[a\left(a-2\right)+\left(a-2\right)\right]\)

\(=\left(a+4\right)\left(a-2\right)\left(a+1\right)\)

---------------------------------

\(2x^2-5x+2\)

\(=2x^2-4x-x+2\)

\(=\left(2x^2-4x\right)-\left(x-2\right)\)

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

\(=\left(x-2\right)\left(2x-1\right)\)

-----------------------------------------

\(x^2-2x-4y^2-4y\)

\(=\left(x^2-4y^2\right)-\left(2x-4y\right)\)

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

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

-------------------------------------

\(a^2-1+4b-4b^2\)

\(=a^2-\left(1-4b+4b^2\right)\)

\(=a^2-\left(1-2b\right)^2\)

\(=\left(a-1+2b\right)\left(a+1-2b\right)\)

----------------------------------------

\(a^4+6a^2b+9b^2-1\)

\(=\left(a^4+6a^2b+9b^2\right)-1\)

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

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

---------------------------------

\(2x^3+16y^3\)

\(=2\left(x^3+8y^3\right)\)

\(=2\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)

Lần sau ghi đề tách riêng từng câu ra nhé em. Ghi dính chùm vậy khó nhìn lắm. Sẽ ít ai giải cho em

1. 2x(3x² - 5x + 3) = 6x³ - 10x² + 6x

2. \(-\dfrac{1}{2}x^2\left(2x^3-4x+3\right)=-x^5+2x^3+\dfrac{-3}{2}x^2\)

3. -2x(x² + 5x - 3) = -2x³ - 10x² + 6x

4. x(3x² - 2x + 5) = 3x³ - 2x² + 5x

5. 3xy²(2x - 4y + 3xy) = 6x²y² - 12xy³ = 9x²y³

Tham khảo

https://hoc247.net/hoi-dap/ngu-van-6/nhan-vat-tu-su-thuong-duoc-mieu-ta-qua-nhung-phuong-dien-nao-faq78788.html

giúp mình với

a: \(3x^2-3xy-5x+5y\)

\(=3x\left(x-y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(3x-5\right)\)

c: \(xz+yz-5x-5y\)

\(=z\left(x+y\right)-5\left(x+y\right)\)

\(=\left(x+y\right)\left(z-5\right)\)

\(3x\left(x-2\right)=3x.x-3x.2=3x^2-6x\)

=> Chọn A

CHọn A

\(2x^3-5x^2+8x-3\)

\(=2x^3-x^2-4x^2+2x+6x-3\)

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

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

2x³-5x²+8x-3=(2x³-x²)-4x²+8x-3=(2x³-x²​)-4x²+2x+6x-3=(2x³-x²​)-(4x²-2x)+(6x-3)

=x²(2x-1)-2x(2x-1)+3(2x-1)=(x²-2x+3)(2x-1)

\(a,\Leftrightarrow\left(5x+1\right)\left(x-4\right)-\left(x-4\right)=0\\ \Leftrightarrow\left(x-4\right)\left(5x+1-x\right)=0\\ \Leftrightarrow5x\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\\ b,\Leftrightarrow2x^2-10x-2x^2-3x=26\\ \Leftrightarrow-13x=26\\ \Leftrightarrow x=-2\\ c,\Leftrightarrow x^3+1-x^3+3x=15\\ \Leftrightarrow3x=14\\ \Leftrightarrow x=\dfrac{14}{3}\)

\(d,\Leftrightarrow x^3-5x+2x^2-10+5x-2x^2-17=0\\ \Leftrightarrow x^3-27=0\\ \Leftrightarrow x^3=27\\ \Leftrightarrow x=3\)