Recall the formula to factor a difference of squares.
a^2- b^2 ⇔ ( a+ b)( a- b)
We can apply this formula to our expression.
x^2- 8^2 ⇔ ( x+ 8)( x- 8)
b To determine if an expression is a perfect square trinomial, we need to ask ourselves three questions.
Is the first term a perfect square?
x^2= x^2 âś“
Is the last term a perfect square?
9= 3^2 âś“
Is the middle term twice the product of 3 and x?
6x=2* 3* x âś“
As we can see, the answer to all three questions is yes! Therefore, we can write the trinomial as the square of a binomial. Note there is a subtraction sign in the middle.
( x^2-6x+9) ⇔ ( x- 3)^2
c To determine if an expression is a perfect square trinomial, we need to ask ourselves three questions.
Is the first term a perfect square?
4x^2= 2^2x^2=( 2x)^2 âś“
Is the last term a perfect square?
1= 1^2 âś“
Is the middle term twice the product of 1 and 2x?
4x=2* 1* 2x âś“
As we can see, the answer to all three questions is yes! Therefore, we can write the trinomial as the square of a binomial. Note there is an addition sign in the middle.
( 4x^2+4x+1) ⇔ ( 2x+ 1)^2
d Look closely at the expression 4x^2-49. It can be expressed as the difference of two perfect squares.
Recall the formula to factor a difference of squares.
a^2- b^2 ⇔ ( a+ b)( a- b)
We can apply this formula to our expression.
( 2x)^2- 7^2 ⇔ ( 2x+ 7)( 2x- 7)
