Video: Expanding a Difference of Two Squares

Rhodri Jones

Use the difference of two squares identity to expand (3𝑎 + 7)(3𝑎 − 7).

01:23

Video Transcript

Use the difference of two squares identity to expand three 𝑎 plus seven multiplied by three 𝑎 minus seven.

Our first thought when asked to expand two brackets or parentheses might be to use the FOIL method. This involves multiplying the first terms in the parentheses. Then, we multiply the outside terms in the parentheses. Thirdly, we multiply the inside terms. And finally, we multiply the last terms in the parentheses.

However, this question asked us to use the difference of two squares identity. The difference of two squares identity tells us that 𝑥 plus 𝑦 multiplied by 𝑥 minus 𝑦 is equal to 𝑥 squared minus 𝑦 squared. In this case, our 𝑥 term is three 𝑎 and our 𝑦 term is seven.

Three 𝑎 multiplied by three 𝑎 is nine 𝑎 squared. And seven multiplied by seven is equal to 49. This means that three 𝑎 plus seven multiplied by three 𝑎 minus seven is equal to nine 𝑎 squared minus 49.

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