Sum/Diff Cubes and PST Brett Solberg AHS ‘11-’12.

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Presentation transcript:

Sum/Diff Cubes and PST Brett Solberg AHS ‘11-’12

Factor the Following 1) 3x2y + 18xz 2) 49x2 – 9y2 3) 3x2 - 147 We will review a few problems from each section.

Today’s Agenda Factor By: Greatest Common Factor GCF Difference of Squares Sum and Difference of Cubes Perfect Square Trinomials

Factoring Sum/Difference of Cubes a3 + b3 = (a + b)(a2 – ab + b2) 8 + y3 a = 2 b = y (2 + y)(4 – 2y + y2) a3 - b3 = (a - b)(a2 + ab + b2) 27x3 – 64 a = 3x b = 4 (3x – 4)(9x2 + 12x + 16)

When to use Sum/Diff Cubes Binomial Subtraction or Addition Perfect Cubes

Examples 1) x3 – 1 a = x b = 1 (x – 1)(x2 + x + 1) 6) 1000x3 – 27 a = 10x b = 3 (10x – 3)(100x2 + 30x – 729) 9) 54y4 – 128y 2y(27y3 – 64) a = 3y b = 4 2y(3y – 4)(9y2 + 12y + 16)

Perfect Square Trinomials PST (a + b)2 = a2 + 2ab + b2 (2x + 1)2 = 4x2 + 4x + 1 (a – b)2 = a2 – 2ab + b2 (2x – 5)2 = 4x2 – 20x + 25

When to use Perfect Square Trinomials First and last terms perfect squares Middle term twice the product of the square roots of outside terms.

Examples 1) 4x2 + 20x + 25 a = 2x b = 5 (2x + 5)2 8) x2 – 18x + 81 a = x b = 9 (x – 9)2 15) 5x2 – 30x + 45 5(x2 – 6x + 9) 5(x – 3)2

Class Assignment Sum/Diff of Cubes Worksheet Perfect Square Trinomial Worksheet