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\(a,=5x\left(4x-1\right)\\ b,=y^2-\left(x-1\right)^2=\left(y-x+1\right)\left(y+x-1\right)\\ c,=6x^2+3x-4x-2=3x\left(x+2\right)-2\left(x+2\right)=\left(3x-2\right)\left(x+2\right)\)
\(a,=5\left(x-2y\right)\\ b,=3xy\left(x-2y\right)\\ c,=\left(x-y\right)\left(x+3\right)\\ d,=\left(x-1\right)\left(2x-4x^2\right)=2x\left(1-2x\right)\left(x-1\right)\\ e,=\left(x-2y\right)^2\\ f,=\left(3x-4y\right)\left(3x+4y\right)\\ g,=\left(x-3\right)\left(x^2+3x+9\right)\)
a. 5x - 10y
= 5(x - 2y)
b. 3x2y - 6xy2
= 3xy(x - 2y)
c. x(x - y) - 3(y - x)
= x(x - y) + 3(x - y)
= (x + 3)(x - y)
d. 2x(x - 1) + 4x2(1 - x)
= 2x(x - 1) - 4x2(x - 1)
= (2x - 4x2)(x - 1)
= 2x(1 - 2x)(x - 1)
e. x2 - 4xy + 4y2
= (x - 2y)2
f. 9x2 - 16y2
= (3x - 4y)(3x + 4y)
g. x3 - 27
= (x - 3)(x2 + 3x + 9)
\(a,=4\left(x-5y\right)\\ b,=5x\left(x+y\right)-\left(x+y\right)=\left(5x-1\right)\left(x+y\right)\\ c,=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
a) \(14x^2y-21xy^2+28x^2y^2\)
\(=7xy\left(2x-3y+4xy\right)\)
b) \(3x^2-5x-3xy+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
c) \(5a^3-20a\)
\(=5a\left(a^2-4\right)\)
\(=5a\left(a-2\right)\left(a+2\right)\)
d) \(2x+2y+x^2+2xy+y^2\)
\(=2\left(x+y\right)\left(x+y\right)^2\)
= \(=\left(x+y\right)\left(2+x+y\right)\)
a) \(x^2+5x+4==x\left(x+1\right)+4\left(x+1\right)=\left(x+1\right)\left(x+4\right)\)
b) \(3x^2+4x-7=3x\left(x-1\right)+7\left(x-1\right)=\left(x-1\right)\left(3x+7\right)\)
c) \(x^2+7x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)
c. x2 - 5x + 4
= x2 + x + 4x + 4
= x(x + 1) + 4(x + 1)
= (x + 4)(x + 1)
a, x2-5xy+2x-10y = (x2 + 2x)-(5xy+10y)
= x(x+2)-5y(x+2)
= (x+2)(x-5y)
b, x2-5x+4 = x2- x - 4x +4
= (x2-x)-(4x-4)
=x(x-1)-4(x-4)
=(x-1)(x-4)
\(a,x^2-5xy+2x-10y\)
\(=\left(x^2-5xy\right)+\left(2x-10y\right)\)
\(=x\left(x-5y\right)+2\left(x-5y\right)\)
\(=\left(x-5y\right)\left(x+2\right)\)
\(b,x^2-5x+4\)
\(=x^2-4x-x+4\)
\(=x\left(x-4\right)-\left(x-4\right)\)
\(=\left(x-1\right)\left(x-4\right)\)