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## College Algebra

### Course: College Algebra>Unit 4

Lesson 6: Factoring quadratics with perfect squares

# Identifying perfect square form

Sal shows how we can identify that a trinomial has the "perfect square" form.

## Want to join the conversation?

• Can the answer also be negative?(-5x-2)?
• If you mean (-5x-2)^2, then yes, but -5x-2 is not the same.
• Is possible to factor this quadratic:
25x^2 + 16x + 9 as (a + b)^2 or in anyway?
• No it wouldn't work.
Yes... your quadratic has perfect squares at both ends, but the middle term is incorrect.
The terms on the ends of your factors would need to be: (5x + 3)^2
If you multiply this out, you get: 25x^2 + 30x + 9

Hope this helps.
• This seems sort of complicated... Why don't we just factor the binomial like we usually would? Like for example, when Sal had 25x^2 + 20x + 4, I did it normally and got the same answer that he did, (5x+2)^2.
• When in life am I ever going to use this stuff?
• ya fr
(1 vote)
• How is Sal so good at writing with a mouse?
(1 vote)
• He uses a stylus (like a pen).
• At the numbers in the brackets are multiplied by each other how does this work?
• I'm a bit confused about the second term in the perfect square form.

In this video, Sal said that 20x (the center term of 25x^2 + 20x + 4) is 2.A.B.x, implying that A is the coefficient of 25^2 and x was just added on because that's how the formula works.

However, in the "Practice: Perfect Squares" exercise, a solution says that 14x (the center term of x^2 + 14x + 49) is twice the root of 1x^2 and 49, implying that A is the coefficiant AND the variable of 1x^2.

Can someone please explain which one is correct, if both are, or if I messed something up? I'm not sure if this matters much, but it confused me when I got to Completing the Square in the next unit.
• Consider what happens when you multiply: (ax+b)(ax+b)
You get: (ax)^2+abx+abx+b^2 which simplifies to a^2x^2+2ab+b^2
The "a" refers to the square root of the coefficient of the x^2 term. The "b" refers to the square root of the constant term.
For 25x^2 + 20x + 4: a=5 and b=2. 2ab = 2(5)(2) = 20
For x^2 + 14x + 49: a=1 and b=7. 2ab = 2(1)(7) = 7

Hope this helps.
• Why is it 2ABx and not ABx^2 @?
(1 vote)
• It is 2ABx because he is adding not multiplying. If Sal were to multiply ABx by ABx the result would be (ABx)^2.