Video: Expanding a Perfect Square

Expand (2𝑥 + 5)².

01:32

Video Transcript

Expand two 𝑥 plus five all squared.

Squaring a number is the same as multiplying it by itself. Therefore, to expand two 𝑥 plus five all squared, we must first rewrite it as two 𝑥 plus five multiplied by two 𝑥 plus five.

In order to expand these two parentheses or brackets, we’ll use the FOIL method. We’ll firstly multiply the first terms. Then, we’ll multiply the outside terms, then the inside, and finally the last terms.

Multiplying the first terms, two 𝑥 multiplied by two 𝑥 gives us four 𝑥 squared. Multiplying the outside terms, two 𝑥 multiplied by positive five gives us positive 10𝑥. In the same way, multiplying the inside terms, positive five and two 𝑥, also gives us positive 10𝑥. Finally, multiplying the last terms, positive five multiplied by positive five gives us positive 25.

We can then simplify or group the middle terms positive 10𝑥 plus 10𝑥 is equal to positive 20𝑥. Therefore, our expansion is four 𝑥 squared plus 20𝑥 plus 25. This is an example of expanding a perfect square.

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