• Section 5.4 in the textbook– Multiply by monomials– Multiply binomials– Square binomials– Multiply (a + b)(a – b)– Multiply more than two polynomials
Multiplying by a Monomial
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Multiplying by a Monomial
• Use the distributive property
• Simplify using exponent rules
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Multiplying by a Monomial (Example)
Ex 1: Multiply: xxx 29 32
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Multiplying by a Monomial (Example)
Ex 2: Multiply: 7442 2634 xyxyyx
Multiply Binomials
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Multiplying Polynomials in General
• To multiply (4x + 3)(2x2 – 3x + 7), we use the distributive property= 4x(2x2 – 3x + 7) + 3(2x2 – 3x + 7)
• Simplify and combine any like terms
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Multiplying Polynomials in General (Example)
Ex 3: Multiply (3x2 + 4x – 5)(3x + 2)
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Multiplying Binomials
• Recall that a binomial is a polynomial with 2 terms
• Can also use the distributive property• A helpful pneumonic is FOIL (essentially
the distributive property)F irstO uterI nnerL ast
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Multiplying Binomials (Example)
Ex 4: Multiply: (4x + 5)(3x - 2)
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Multiplying Binomials (Example)
Ex 5: Multiply: (2x - 7)(x - 8)
Square Binomials
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Square Binomials
• First expand: (a + b)2 = (a + b)(a + b)
• Finally use FOIL
• Do NOT just square each of the individual terms!
(a + b)2 ≠ a2 + b2
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Square Binomials (Example)
Ex 6: Multiply: (3x + 2y)2
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Square Binomials (Example)
Ex 7: Multiply: (4x – 5)2
Multiply (a + b)(a – b)
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Multiply (a + b)(a – b)
• A special product
• Use FOIL to simplify
• The O and the I terms cancel
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Multiply (a + b)(a – b) (Example)
Ex 8: Multiply (m – 3n)(m + 3n)
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Multiply (a + b)(a – b) (Example)
Ex 9: Multiply (2r4 + 5s2)(2r4 – 5s2)
Multiply More than Two Polynomials
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Multiply More than Two Polynomials
• Multiply the first two polynomials using the techniques discussed thus far
• Use the distributive property to multiply the result by the last polynomial
• Simplify
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Multiply More than Two Polynomials (Example)
Ex 10: Multiply (x + 2)(x – 7)(x + 1)
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Multiply More than Two Polynomials (Example)
Ex 11: Multiply (x + 4)2(7x – 2)
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Summary
• After studying these slides, you should know how to do the following:– Multiply by monomials– Multiply binomials– Square binomials– Multiply (a + b)(a – b)– Multiply more than two polynomials