Question Video: Factorising the Difference of Two Squares Mathematics

Video Transcript

Completely factor 16𝑎 squared 𝑏 squared minus 49.

This would be considered a difference of squares. And we know that for a difference of squares, 𝑎 squared minus 𝑏 squared, it factors to be 𝑎 plus 𝑏 times 𝑎 minus 𝑏. So for our expression, so for our expression we need to make sure we have the subtraction sign because it’s a difference of squares.

And since we have the subtraction sign, now we can move on to finding 𝑎 and 𝑏. So in order to get from 𝑎 squared in the expression to 𝑎 in a factorized form, we would need to square root 𝑎 squared to get 𝑎 and square root 𝑏 squared to get 𝑏. So we need to do that for our expression. So if we would take the square root of 16𝑎 squared 𝑏 squared, the square root of 16 is four, the square root of 𝑎 squared is 𝑎, and the square root of 𝑏 squared is 𝑏.

So here would be 𝑎. And for 𝑏, the square root of 49 is seven. So seven is 𝑏. So now all we need to do is to plug in four 𝑎𝑏 for 𝑎 in a factorized form and seven in for 𝑏 into the factorized form. So we would have 16𝑎 squared 𝑏 squared minus 49 would be equal to four 𝑎𝑏 plus seven times four 𝑎𝑏 minus seven.

It won’t matter if we would put the four 𝑎𝑏 minus seven first instead of the four 𝑎𝑏 plus seven as long as we have the plus and the minus in our final answer. So once again, our final answer after factoring would be four 𝑎𝑏 plus seven four 𝑎𝑏 minus seven multiplied together.