Question

How do you multiply `(4a+b)^2`?

Answer 1

`16a^2+8ab+b^2`

Explanation:

We can express `(4a+b)^2` as `(4a+b)(4a+b)`

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket.

This may be done as follows.

`(color(red)(4a+b))(4a+b)=color(red)(4a)(4a+b)color(red)(+b)(4a+b)`

distribute the brackets.

`rArr16a^2+4ab+4ab+b^2`

collecting like terms gives `16a^2+8ab+b^2`

`rArr(4a+b)^2=16a^2+8ab+b^2`