Mishita Dharia - Quadratics
Factoring Difference of Squares and Perfect Squares
Perfect Square Trinomials: The product of a squared binomial is a perfect square trinomial.
Recall:
(a + b)^2 = (a + b)(a + b) = a^2 + 2ab + b^2
(a – b)^2 = (a – b)(a – b) = a^2 – 2ab + b^2
So…
In order to go from a^2 – 2ab + b^2 to (a + b)^2 we must square root the first term and square root the last term while make sure that the sign in the binomial corresponds with the sign in front of the middle term.
Let’s do an example…
Factor the following: 25x^2+ 20x + 4.
When we square root the first term, and square root the last term while make sure that the sign in the binomial corresponds with the sign in front of the middle term, we get…
= (5x + 2) ^2
Now you try…
Factor the following: 9x^2 – 62 + 49
Answer…
(3x - 7) ^2
Perfect Square Trinomials: The The product of a sum and a difference is a difference of two squares.
Recall:
(a + b)(a – b) = a^2 – b^2
(a – b)(a + b) = a^2 – b^2
So…
In order for us to go from a^2 – b^2 to (a + b)^2 we must square root the terms and multiply them together as a sum and a difference, so that the last term is negative, otherwise it would be positive.
Let’s do an example…
Factor the following: 29x^2 – 4
When we square root the terms, we must multiply them together as a sum and a difference...
=(3x +2)(3x-2)
Now you try…
Factor the following: 25x^2 – 64
Answer…
(5x + 8) (5x – 8)
Extra Practice…