Perfect Squares | cutecute

Perfect Squares.

Perfect Squares is another way of factoring trinomials (3 terms).

Perfect Square trinomial can be factored using this pattern.

a^2 + 2ab + b^2 = ( a + b)^2

a^2 - 2ab + b^2 = ( a - b)^2

In perfect square , your first and last terms are perfect squares and so the middle term is the product of square roots of the first and last term multiplied by 2.

For example; x^2 + 14x + 49

When you factor the equation above. You know that your answer must be in two brackets.

( ) ( )

Here the since there is no number in front of the variable, it means the variable has a coefficient of 1. So now you would put the factors of 1x^2 in the two brackets.

Find the square root of the first and last number.

x^2 = x times x

49= 7 times 7

So now when you find the 2 numbers you put them in the brackets.

( x+7) (x+ 7)

Simply.

( x+7) ^2

The trinomial that results from squaring a binomial is called a PERFECT SQUARE trinomial.

Example #2 4g^2 + 28g + 49

2g x 7 = 14g x 2 = 28g Which is your middle term.

Solution: (2g + 7) ( 2g +7)

Simply : (2g + 7) ^2

To check your answer simply expand the answer,

(2g +7)^2

= (2g +7) (2g +7)

= 4g^2 +14g +14g + 49

= 4g^2 +28 g +49

So once you get the equation you started with, that means your answer is correct.

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