Video: Factorising the Difference of Two Squares

Completely factor 16π‘ŽΒ²π‘Β² βˆ’ 49.

01:45

Video Transcript

Completely factor 16π‘Ž squared 𝑏 squared minus 49.

This would be considered a difference of squares. And we know that for a difference of squares, π‘Ž squared minus 𝑏 squared, it factors to be π‘Ž plus 𝑏 times π‘Ž 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 π‘Ž and 𝑏. So in order to get from π‘Ž squared in the expression to π‘Ž in a factorized form, we would need to square root π‘Ž squared to get π‘Ž 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 16π‘Ž squared 𝑏 squared, the square root of 16 is four, the square root of π‘Ž squared is π‘Ž, and the square root of 𝑏 squared is 𝑏.

So here would be π‘Ž. 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 π‘Žπ‘ for π‘Ž in a factorized form and seven in for 𝑏 into the factorized form. So we would have 16π‘Ž squared 𝑏 squared minus 49 would be equal to four π‘Žπ‘ plus seven times four π‘Žπ‘ minus seven.

It won’t matter if we would put the four π‘Žπ‘ minus seven first instead of the four π‘Žπ‘ 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 π‘Žπ‘ plus seven four π‘Žπ‘ minus seven multiplied together.

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