Question

Answer 1

\(a,6x^2-x=x\left(6x-1\right)\\ -----\\ b,x^2+2x+1-4y^2=\left(x^2+2x+1\right)-4y^2=\left(x+1\right)^2-4y^2=\left[\left(x+1\right)-2y\right]\left[\left(x+1\right)+2y\right]=\left(x+1-2y\right)\left(x+2y+1\right)\\ -----\\ c,x^2+5x-xy-5y=x\left(x+5\right)-y\left(x+5\right)=\left(x-y\right)\left(x+5\right)\)

Answer 2

`a, 6x^2 - x = x(6x-1)`

`x^2 + 2x + 1 - 4y^2 = (x+1)^2 - (2y)^2 = (x+1-2y)(x+1+2y)`

`c, x^2 + 5x - xy - 5y = x(x+5) - y(x+5)`

`= (x-y)(x+5)`

Answer 3

\(a, 6x^2-x=x\left(6x-1\right)\)
\(b, x^2+2x+1-4y^2\) \(=\left(x+1\right)^2-4y^2=\left(x+1-2y\right)\left(x+1+2y\right)\)
\(c, x^2+5x-xy-5y=x^2-xy+5x-5y=x\left(x-y\right)+5\left(x-y\right)=\left(x+5\right)\left(x-y\right)\)

Answer 4

a) 6x^2-x
=x(6x-1)

b)x^2+2x+1-4y^2

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

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

c)x^2+5x-xy-5y

=x(x-y)+5(x-y)

=(x+5)(x-y)

Answer 5

a) 6x² - x

= x(6x - 1)

b) x² + 2x + 1 - 4y²

= (x² + 2x + 1) - (2y)²

= (x + 1)² - (2y)²

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

c) x² + 5x - xy - 5y

= (x² - xy) + (5x - 5y)

= x(x - y) + 5(x - y)

= (x - y)(x + 5)