Special Cases of Multiplying Polynomials

Friday, September 13, 2013

Squaring Binomials results in Perfect Square Trinomials

1. Square the first term. 2. Double the product of the two terms. 3. Square the last term. Ex: (2x – 1)2

4x2 - 4x + 1 Perfect square trinomial

Ex: (3x + 4)2

9x2 + 24x + 16 Perfect square trinomial

Sum times Difference of same terms results in Difference of Perfect Squares

1. Multiply the first term. 2. Multiply the last terms. Ex: (2x – 1) (2x + 1) 4x2 – 1 Difference of Perfect

Squares Ex: (3x + 4) (3x – 4) 9x2 – 16 Difference of Perfect

Squares (This is because the middle terms cancel.)

(a + b)(a2 – ab + b2) Results in Sum of Perfect Cubes

1. Cube 1st term in binomial 2. Cube 2nd term in binomial Ex: (2x + 3) (4x2 – 6x + 9) 8x3 + 27 Ex: (x + 1) (x2 – x +1) x3 + 1 (Again, middle terms cancel out.) (plus, minus, plus gives plus)

(a – b)(a2 + ab + b2)Results in Difference of Perfect Cubes

1. Cube 1st term in binomial 2. Cube 2nd term in binomial Ex: (2x - 3) (4x2 + 6x + 9) 8x3 - 27 Ex: (x – 1) (x2 + x +1) x3 – 1 (Again, middle terms cancel out.) (minus, plus, plus gives minus)

Classwork 30 practice problem worksheet with special case binomials

Homework12 problem worksheet with special case binomials

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