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a: =2(x-2)+y(x-2)
=(x-2)(2+y)
b: \(=\left(x+y\right)^2-4=\left(x+y+2\right)\left(x+y-2\right)\)
c: =(x-7)(x+2)
a.
2x - 4 + xy - 2y
= 2(x-2) +y(x-2)
= (x-2)(y+2)
c.
x^2 - 5x - 14
= x^2 + 2x - 7x - 14
= x(x+2) - 7(x+2)
= (x-7)(x+2)
a) \(\left(x^2+4x+8\right)^2+3x\left(x^2+4x+8\right)+2x^2\)
= \(\left(x^2+4x+8\right)^2+x\left(x^2+4x+8\right)+2x\left(x^2+4x+8\right)+2x^2\)
= \(\left(x^2+4x+8\right)\left(x^2+4x+8+x\right)+2x\left(x^2+4x+8+x\right)\)
= \(\left(x^2+6x+8\right)\left(x^2+5x+8\right)\)
= \(\left(x^2+2x+4x+8\right)\left(x^2+5x+8\right)\)
= \(\left(x+2\right)\left(x+4\right)\left(x^2+5x+8\right)\)
Bài 1:
a: Ta có: \(\left(6x+3\right)-\left(2x-5\right)\left(2x+1\right)\)
\(=\left(2x+1\right)\left(3-2x+5\right)\)
\(=\left(2x+1\right)\left(8-2x\right)\)
\(=2\left(4-x\right)\left(2x+1\right)\)
b) Ta có: \(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\left(3x-2\right)\left(3x-6\right)\)
\(=3\left(3x-2\right)\left(x-2\right)\)
Bài 2:
a: Ta có: \(\left(a-b\right)\left(a+2b\right)-\left(b-a\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b\right)+\left(a-b\right)\left(2a-b\right)-\left(a-b\right)\left(a+3b\right)\)
\(=\left(a-b\right)\left(a+2b+2a-b-a-3b\right)\)
\(=\left(a-b\right)\left(2a-4b\right)\)
\(=2\left(a-b\right)\left(a-2b\right)\)
f: Ta có: \(x^2-6xy+9y^2+4x-12y\)
\(=\left(x-3y\right)^2+4\left(x-3y\right)\)
\(=\left(x-3y\right)\left(x-3y+4\right)\)
Ta có: M = xy(x+y) + yz(y+z) + xz (x+z) + 2xyz
= xy(x + y) + yz(y + z) + xyz + xz(x + z) + xyz
= xy(x + y) + yz(y + z + x) + xz(x + z + y)
= xy(x + y) + z(x + y + z)(x + y)
= (x + y)(xy + zx + zy + z2)
= (x + y)[x(y + z) + z(y + z)]
M = (x + y)(y + z)(z + x) (đpcm)
a) \(=\left(2x-1\right)^2\)
b) \(=x\left(y^2-x^2+2x-1\right)=x\left[y^2-\left(x-1\right)^2\right]=x\left(y-x+1\right)\left(y+x-1\right)\)
a
Ta có
\(2x^2+2x=2x\left(x+1\right)\)
b
\(\left(1+xy\right)^2-\left(x+y\right)^2=\left(1+xy-x-y\right)\left(1+xy+x+y\right)\)
\(\left[\left(1-x\right)-y\left(1-x\right)\right]\left[\left(1+x\right)+y\left(1+x\right)\right]=\left(1-x\right)\left(1-y\right)\left(1+x\right)\left(1+y\right)\)