Question

Factor:j) x(x+2) + y (x + 2) - 5(x + 2)k) 5y2 - 10y3l) ax + ay + az

Answer 1

Given:

`x\left(x+2\right)+y(x+2)-5\left(x+2\right)`

Required:

We need to factorize the given expressions.

Step-by-step explanation:

`x\left(x+2\right)+y(x+2)-5\left(x+2\right)`

The common multiple in all terms is (x+2).

Take out the common term (x+2).

`x\left(x+2\right)+y(x+2)-5\lparen x+2)=(x+2)(x+y-5)`

Final answer:

`\begin{equation*} (x+2)(x+y-5) \end{equation*}`

K)

Given:

`5y^2-10y^3`

Step-by-step explanation:

The given expression can be written as follows.

`5y^2-10y^3=5y^2-5*2* y^2* y`

`5y^2-10y^3=5y^2-5y^2*2y`
`\text{ The common multiple in all terms is }5y^2.`
`\text{ Take out the common term }5y^2.`

`5y^2-10y^3=5y^2(1-2y)`

Final answer:

`5y^2(1-2y)`

l)

Given:

`ax+ay+az`

Step-by-step explanation:

`\text{ The common multiple in all terms is }a.`

`\text{ Take out the common term }a.`

`ax+ay+az=a(x+y+z)`

Final answer:

`a(x+y+z)`