Post on 22-Sep-2020
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I CAN multiply polynomials by monomials.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Remember that when you multiply two powers with the same bases, you add the exponents. To multiply two monomials, multiply the coefficients and add the exponents of the variables that are the same.
(5m2n3)(6m3n6) = 5 · 6 · m2+3n3+6 = 30m5n9
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Multiply.
Additional Example 1: Multiplying Monomials
A. (2x3y2)(6x5y3)
B. (9a5b7)(–2a4b3)
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Try This: Example 1
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Multiply. A. (5r4s3)(3r3s2)
B. (7x3y5)(–3x3y2)
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
To multiply a polynomial by a monomial, use the Distributive Property. Multiply every term of the polynomial by the monomial.
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Multiply.
Additional Example 2A & 2B: Multiplying a Polynomial by a Monomial
A. 3m(5m2 + 2m)
B. –6x2y3(5xy4 + 3x4)
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Multiply.
Additional Example 2C: Multiplying a Polynomial by a Monomial
C. –5y3(y2 + 6y – 8)
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Try This: Example 2A & 2B
Multiply.
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A. 4r(8r3 + 16r)
B. –3a3b2(4ab3 + 4a2)
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
Try This: Example 2C
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Multiply.
C. –2x4(x3 + 4x + 3)
Pre-Algebra
13-5 Multiplying Polynomials by Monomials
I CAN multiply binomials.
Pre-Algebra
13-6 Multiplying Binomials
Vocabulary FOIL
Insert Lesson Title Here
Pre-Algebra
13-6 Multiplying Binomials
You can use the Distributive Property to multiply two binomials.
(x + y)(x +z) = x(x + z) + y(x + z) = x2 + xz + xy + yz
Pre-Algebra
13-6 Multiplying Binomials
The product can be written as FOIL: The First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.
2 First Last
Inner Outer
Pre-Algebra
13-6 Multiplying Binomials
Multiply.
Additional Example 1A & 1B: Multiplying Two Binomials
A. (n – 2)(m – 8) B. (x + 3)(x + z)
Pre-Algebra
13-6 Multiplying Binomials
Additional Example 1C & 1D: Multiplying Two Binomials
Multiply. C. (a + 3)(a + 5) D. (x – 4y)(x + 7y)
Pre-Algebra
13-6 Multiplying Binomials
When you multiply two binomials, you will always get four products. Then look for like terms to combine.
Helpful Hint
Pre-Algebra
13-6 Multiplying Binomials
Try This: Example 1A & 1B
Insert Lesson Title Here
Pre-Algebra
Multiply. A. (r – 4)(s – 6) B. (y + 2)(y + r)
13-6 Multiplying Binomials
Try This: Example 1C & 1D
Insert Lesson Title Here
Pre-Algebra
Multiply. C. (a + 3)(a + 4) D. (x – 3y)(x + 8y)
13-6 Multiplying Binomials
Multiply.
Additional Example 3A & 3B: Special Products of Binomials
A. (x + 6)2 B. (n – m)2
13-6 Multiplying Binomials
Try This: Example 3C
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C. (x – y)(x + y)
Multiply.
13-6 Multiplying Binomials