Question

Factorise $ax+bx-ay-by$
A. $\left( x+y \right)\left( a+b \right)$
B. $\left( x-a \right)\left( a+y \right)$
C. $\left( x-y \right)\left( a+b \right)$
D. $\left( x+a \right)\left( a-y \right)$

Answer 1

Hint: In this problem we need to factorize the given expression. We can observe that the first two terms of the expression have a common term $x$, so we will take $x$ as common from the first two terms. We can also observe that the last two terms of the expression have a common term $-y$, so we will take $-y$ as common from the last two terms. Now we can observe the common term $\left( a+b \right)$ in the expression. So, we can take the term $\left( a+b \right)$ as common from the expression to get the required result.

Complete step-by-step answer:
Given expression is $ax+bx-ay-by$.
The first two terms of the above expression are $ax+bx$. In the first two terms we have the common term $x$. So, taking $x$ as common from the first two terms, then we will get
$ax+bx=x\left( a+b \right)$
The last two terms of the given expression are $-ay-by$. In the last two terms we have the common term $-y$. So, taking $-y$ as common from the last two terms, then we will get
$-ay-by=-y\left( a+b \right)$
From above two values, then given expression is modified as
$ax+bx-ay-by=x\left( a+b \right)-y\left( a+b \right)$
In the above equation we have the common term $\left( a+b \right)$ in the left-hand side, then we will have
$ax+bx-ay-by=\left( x-y \right)\left( a+b \right)$

So, the correct answer is “Option C”.

Note: We can also solve this problem in another method. We will calculate the product of each term in the given options by using the distribution law of multiplication. After getting the products from each option we will compare the products with the given expression and check which option is the correct one. This method is not the easiest one and it will take much time to get the result.