Squaring a Binomial x32 n n n n

Squaring a Binomial (x+3)2 n n n n How many terms do you get when you square a binomial? 3 Why don’t you just get two terms? (x+3)2 Why isn’t the answer x 2+9? Squaring a binomial means multiplying a binomial by itself. (x+3)2=(x+3) This indicates four multiplications.

Squaring a Binomial (x+3)2 n n (x+3)2=(x+3) Therefore, there are four multiplications. The same as using the FOIL method. x 2+3 x+3 x+9 x 2+6 x+9

Squaring a Binomial n n n n Let’s look at several examples: (x+4)2= (x+4) x 2+4 x+4 x+16 x 2+8 x+16 (x-9)2= (x-9) x 2 -9 x-9 x+81 x 2 -18 x +81 (2 x-3 y)2= (2 x-3 y) 4 x 2 -6 xy+9 y 2 4 x 2 -12 xy+9 y 2

Squaring a Binomial n n n n As you saw in the last slide, the same pattern repeats each time we square a binomial. Therefore, it is easy to learn the three steps of squaring a binomial instead of rewriting the problem every time and using the FOIL method. Here are three steps: (x+5)2 1. Square the first term. x 2 2. Multiply the first term by the second term and do it again. This step is the same as doing the outside and inside steps in the FOIL method. 5 x+5 x Since the you will always get the same result twice, just multiply the terms and double the result or simply multiply the result by 2. 2(5 x)= 10 x 3. Square the last term. 25 Answer: x 2+10 x+25 To review: Since you get the same two terms each time you do the second step the terms always combine. In this case we get 2(5 x) or 10 x. So the answer is always THREE terms.

Let’s Practice (x-5)2 n n n n n The three steps of squaring a binomial are Square the first term. x 2 Multiply the two terms and double the result. 2(-5 x)=-10 x Square the last term. +25 Answer: x 2 -10 x+25

Practice (x+3)2 n n n n Square the first term. x 2 Multiply the two terms and double the result. 2(+3 x)=6 x Square the last term. +9 Answer: x 2+6 x+9

Practice (x-6)2 n n n n Square the first term. x 2 Multiply the two terms and double the result. 2(-6 x)=-12 x Square the last term. +36 Answer: x 2 -12 x+36