Perfect Square Trinomial By: Mr.Jay Mar Bolajo

Recall: (Square of a Binomial) (y+5)2 =

Answer y2 + 10y + 25

( x – 8 )2

Answer x2 – 16x + 64

(a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2 Recall: Pattern for square of a binomial (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 – 2ab + b2

Perfect Square Trinomial a2 + 2ab + b2 = ( a + b )2 a2 – 2ab + b2 = ( a – b )2

Get the square root of the first term. Get the square root of the last term.

In factoring a perfect square trinomial, see to it that the first term and the last terms of a trinomial are both squares and the middle term is twice the product of the square root of both the first term and the last terms of the given trinomial.

Therefore, getting the square roots of these perfect squares give the terms of the binomial and express them as a sum or difference depending the sign of the middle term.

Examples x2 + 4x + 4 Square root of x2 = x Square root of 4 = 2 Copy the sign of the middle term = + ( x + 2 )2

x2 - 6x + 9 Square root of x2 = x Square root of 9 = 3 Copy the sign of the middle term = - ( x – 3 )2

25x2 + 100x + 100 Square root of 25x2 = 5x Square root of 100 = 10 Copy the sign of the middle term = + (5x + 10)2

Drill Factor the following. 1. y2 – 16y + 64

( y – 8 )2

2. 100y2 + 60y + 9

Answer ( 10y + 3 )2

3. 4x2 – 44x + 121

Answer ( 2x – 11 )2

4. 9x2 – 18x + 9

Answer ( 3x – 3 )2

25x2y2 – 50xy + 25

Answer ( 5xy – 5 )2

Skill Practice Factor completely x2 + 18x + 81 4x2 + 12x + 9 x2 – 6xy + 9y2 25p2 – 60pq + 36 q2 16 – 40n + 25n2

Answers ( x + 9 )2 ( 2x + 3 )2 ( x – 3y )2 ( 5p – 6q )2 ( 4 – 5n )2