Dynamic Activity

Factoring Special Products

Lesson Vocabulary

• perfect-square trinomial
• difference of two squares

Take Note Key Concept: Factoring Perfect-Square Trinomials

Algebra For every real number a and b:

a 2 + 2 a b + b 2 = ( a + b ) ( a + b ) = ( a + b ) 2 eh squared , plus 2 eh b plus , b squared , equals open eh plus b close open eh plus b close equals . open eh plus b close squared

a 2 − 2 a b + b 2 = ( a − b ) ( a − b ) = ( a − b ) 2 eh squared , minus 2 eh b plus , b squared , equals open eh minus b close open eh minus b close equals . open eh minus b close squared

Examples x 2 + 8 x + 16 = ( x + 4 ) ( x + 4 ) = ( x + 4 ) 2 x squared , plus 8 x plus 16 equals open x plus 4 close open x plus 4 close equals . open x plus 4 close squared

4 n 2 − 12 n + 9 = ( 2 n − 3 ) ( 2 n − 3 ) = ( 2 n − 3 ) 2 4 n squared , minus 12 n plus 9 equals open 2 n minus 3 close open 2 n minus 3 close equals . open 2 n minus 3 close squared