Question

Factorise: $ax+bx+ay+by$

• A. $(x+a)(y+b)$
• B. $(x+b)(y+a)$
• C. $(x+y)(a+b)$
• D. $(x+a+b)\left(y\right)$

Answer 1

The correct option is C

$(x+y)(a+b)$

The expression $ax+bx+ay+by$ can be written as

$(ax+ay)+(bx+by)$.....(i)

Taking $a$ common from first two terms and $b$ common from last two terms, expression (i) can be written as

=$\left(a\right(x+y\left)\right)+\left(b\right(x+y\left)\right)$...(ii)

Taking $(x+y)$ common from expression (ii), we get

=$(x+y)(a+b)$

Therefore, the factors of $ax+bx+ay+by$ are $(x+y)$ and $(a+b)$.

i.e.,$ax+bx+ay+by=(x+y)(a+b)$