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Name: ______________________________________ Date:________________ Unit 4 Algebra: Cubic, Square Root, and Rational Functions (Red) Section 3.2 Factoring Cubics Using Special Product Patterns Pages 130-133 Essential Question: How do you factor cubics using special product patterns? Remember: x2 + 2xy + y2 = (x + y)2 Perfect Square Trinomial Perfect Square Trinomial Difference of two squares x – 2xy + y = (x – y) x2 – y2 = (x + y) (x - y) 2 2 2 Vocabulary: Special Product Patterns- there are similar formulas for factoring special cubic polynomials 1. ____________________ = _______ + _______ + _______ + _______ 2. ____________________ = _______ - _______ + ______ - _______ Note: the 2nd and 3rd terms both have 3 as a factor Example 1: SPECIAL PRODUCT PATTERNS 1. Using special product patterns factor the expression by dividing the 2nd and 3rd term by 3 and take the cube root of the 1st and 4th term. x3 + 6x2 + 12x + 8 = Take the cube root (___)3 + (3) __ __ + (3) __ __ + (____)3 Divide by 3 2. Now use the above pattern (see definition) to solve: = (_____ + ____)3 YOU TRY… Factor the expressions: Remember to take the cube root of the 1st and 4th term and divide the 2nd and 3rd term by 3. a) x3 – 12x2 + 48x – 64 = = b) x3 + 3x2 + 3x + 1= = (___)3 - (3) __ __ + (3) __ __ - (____)3 (_____ - ____)3 (___)3 + (3) __ __ + (3) __ __ + (____)3 (_____ + ____)3 Name: ______________________________________ Date:________________ Example 2: FACTOR OUT A GCF FIRST Before factoring using the special products pattern, factor (divide) the GCF first so that the leading coefficient becomes 1 and the degree is 3. 2x3- 6x2 + 6x - 2 = ___ [(___)3 - (3) ____ + (3) ____ - (____)3] = ___(_____ - ____)3 YOU TRY… Factor the expressions: a) -3x3 + 18x2 - 36x + 24 b) x4 + 15x3 + 75x2 + 125x Example 3: FACTORING CUBICS WITH SPECIAL PATTERNS Combine your knowledge of special patterns and factoring the GCF to solve the following problems: a3b3 + 12a2b2 + 48ab + 64 = (___)3 + (3) __ __ + (3) __ __ + (____)3 hint: check to see if you can factor out the GCF, then divide the 2nd & 3rd terms by 3 and take the cube root of the 1st & 4th term. = (_____ + ____)3 hint: use the above patterns to solve 343x3 - 147x2 y+ 21xy2 - y3= (___)3 - (3) ____ + (3) ____ - (____)3 hint: once again, check to see if you can factor out the GCF, then divide the 2nd & 3rd terms by 3 and then take the cube root of the 1st & 4th term. Use the patterns to solve. = (_____ - ____)3 YOU TRY… Factor the expressions: a) 8x3 + 12x2y + 6xy2 + y3 b) p3q3- 18p2q2 + 108pq - 216