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Multiply monomials

Multiply monomials. To multiply a polynomial by a monomial. Multiply the numbers together. Multiply the same letters together by adding the exponents. Ex – 3x 3 y 6 z 8 ( 5x 9 y 4 z 7 )=. 15x 12 y 10 z 15. 16 a 9 b 3 (5a 7 z)=. 80a 16 b 3 z. To multiply a polynomial by a monomial.

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Multiply monomials

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  1. Multiply monomials

  2. To multiply a polynomial by a monomial • Multiply the numbers together • Multiply the same letters together by adding the exponents Ex – 3x3y6z8 ( 5x9y4z7)= 15x12y10z15 16 a9b3(5a7z)= 80a16b3z

  3. To multiply a polynomial by a monomial use the Distributive Property and the Properties of Exponents.

  4. Multiplying a Monomial and a Polynomial Find each product. A. 4y2(y2+ 3) (4y2  y2)+ (4y2 3) Distribute. Multiply. 4y4 + 12y2 B. fg(f4 + 2f3g – 3f2g2 + fg3) Distribute. (fgf4) + (fg 2f3g) – (fg  3f2g2) + (fgfg3) Multiply. f5g + 2f4g2 – 3f3g3 + f2g4

  5. Find each product. a. 3cd2(4c2d– 6cd + 14cd2) Distribute. (3cd2  4c2d)– (3cd2 6cd) + (3cd2 14cd2) Multiply. 12c3d3 – 18c2d3 + 42c2d4 b. x2y(6y3 + y2 – 28y + 30) Distribute. (x2y 6y3) + (x2yy2) – (x2y  28y) + (x2y 30) Multiply. 6x2y4 + x2y3 – 28x2y2 + 30x2y

  6. Laws of Exponents • Quotient of exponents – subtract the exponents an= an-m Bases must be the same am Examples a5 = a3 a5-3 = a2 p5 = p9 p 5-9 = p-4

  7. Laws of Exponents • Power to a Power – multiply the exponents (a)nm = anm Examples (52)3 56 (33a5)4 312a20 = 531441a20 (22s5t7x3)5 210s25t35x15 =1024s25t35x15

  8. Laws of Exponents • Monomial to a power – distribute the exponent (ab)n= anbn Examples (5x)3 53x3 =125x3 (ab)4 a4b4 (2stx)5 25s5t5x5 =32s5t5x5

  9. Example 3B:Using Properties of Exponents to Simplify Expressions Simplify the expression. Assume all variables are nonzero. Quotient of Powers (yz3 – 5)3 = (yz–2)3 Power of a Product y3(z–2)3 Power of a Product y3z(–2)(3) Negative of ExponentProperty

  10. Check It Out! Example 3a Simplify the expression.Assume all variables are nonzero. (5x6)3 53(x6)3 Power of a Product 125x(6)(3) Power of a Power 125x18

  11. Homework Page 355 # 1-28 omit 10 & 11

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