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## Algebra 1

### Course: Algebra 1>Unit 13

Lesson 3: Special products of binomials

# Squaring binomials of the form (x+a)²

Sal introduces perfect square expressions. For example, (x+7)² is expanded as x²+14x+49.

## Want to join the conversation?

• At , Isn't the binomial (x+a)(x+b) = x^2 + (a+b)x +ab? Thanks. • Sal,

Is 2x equivalent to X^2? Logically, it would seem so: 2-X's or X,X (squared), yet, I am relearning math after decades of "dust." I don't assume anything! lol • Has Sal released a video on trinomials? • with an expression like (x+a)^2 why wouldn't you just distribute the exponent to do x^2 + a^2 ? • Exponents represent repetitive multiplication. Thus, the exponent property that distribute the exponent only works when you have factors (items being multiplied or divided). The expression (x+2)^2 contains terms inside the parentheses. So, the exponent properties do not apply.
To simplify (x+2)^2, you need to use distributive property or FOIL. Or, you can learn the pattern as Sal shows at bout into the video. Squaring a binomial creates a perfect square trinomial.
Hope this helps.
• What if we have this kind of expression`(3x+2)^2`, is its form also`x^2+2ax+a^2`? • Almost; in this case you have a factor of 3 along with x, which you also need to take into account. The general form (without x or numbers) is (a+b)^2 = a^2 + 2ab + b^2. In your example a = 3x and b = 2 (I hope it's not too confusing, the b in the general form is the a in the video).
So then a^2 = (3x)^2 = 9x^2; b^2 = 2^2 = 4; and 2ab = 2*3x*2 = 12x.
Putting it all together:
(3x+2)^2 = 9x^2 + 12x + 4.
• In exponents properties, there's this property for taking a power of a product: (x*y)^n=x^n*y^n. But when taking a power of a sum like in this video, I've noticed that it seems to work differently, and I find that confusing. Could anyone clarify? Why isn't it: (x+y)^2 = x^2+y^2? • Well using the distributive property, (x+y)^2 gets distributed to (x+y)(x+y) and then either using the FOIL method you proceed ahead or in the common way which leads up to x^2+2xy+y^2. Instead if you do it x^2+y^2 then it simplifies to (x+y)(x-y),as taught in the previous videos by Sal, which is totally different than your question. Hope I was of some help!
• I don’t find these so called short cuts worth it, you’re likely to misremember it and doing the distributive property takes like 3 more seconds. • I learned a different method, FOIL, does it apply here as well? • What is a binomial? • A binomial is just two terms that don't combine or cancel out. For instance (3x - 2) is a binomial. However, (-x + 2y + 4) and (x^2 + 2x - 1) are not binomials because they have more than two terms.
• can someone explain how sal got the second up to the last step in the pattern? You have to remember that the original expression is `(x + 7)^2`. What the video is saying at , therefore, is that whenever you are Squaring binomials of the form (x+b)^2, the constant term that you get in your final solution will always be the result of raising the constant term from the original expression (`b = 7` in this case) to the second power.