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### Course: Get ready for Algebra 2>Unit 1

Lesson 5: 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.
• Yeah, Sal made a mistake there. It should've been a*b and not b^2
• 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
• 2X = X^2 only if X=2. Then you would have 2(2) = 2(2)
2X means 2 times X or X+X
X^2 means X times X
So, if X = 3, 2X becomes 2(3) = 6 and X^2 become 3(3) = 9
Hope that clarifies things.
• Has Sal released a video on trinomials?
• Sal needs 2 make one if not
• 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.
• You are right that it doesn't save much time in multiplying the 2 binomials. However, when you get to later lessons on factoring quadratics, it can speed up the process. The pattern is also used in converting quadratic equations to vertex form. You also use it with equations of circles. So, it is worth understanding and learning the pattern.
• I learned a different method, FOIL, does it apply here as well?
• FOIL always works, this is just a shortcut is you specifically have a square.
• 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.