Question

Answer 1

\(3x^2y-4xy^2=xy\left(3x-4y\right)\)

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

\(x^2+xy+xz+yz=x\left(x+y\right)+z\left(x+y\right)=\left(x+z\right)\left(x+y\right)\)

\(x^2+4xy-5y^2=x^2-xy+5xy-5y^2=x\left(x-y\right)+5y\left(x-y\right)=\left(x-y\right)\left(x+5y\right)\)

Answer 2

a)

   3x²y - 4xy²

= xy.(3x - 4y)

b)

(x - 2)²-y²

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

c)

x² + xy + xz + yz

= (x²+xy) + (xz + yz)

= x (x + y) + z (x + y)

= (x + y)(x + z)

d)

x² + 4xy - 5y²

= x² - xy + 5xy - 5y²

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

= (x - y)(x + 5y

Answer 3

a: \(=xy\left(3x-4y\right)\)

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

c: \(=x\left(x+y\right)+z\left(x+y\right)=\left(x+y\right)\left(x+z\right)\)

d: \(=x^2+5xy-xy-5y^2=\left(x+5y\right)\left(x-y\right)\)