Multiplying by a Monomial Be able to multiply two monomials or a monomial and a polynomial

FHSPolynomials2 Property 1 of Exponents Let’s look at an example that demonstrates how this property ____________ works: We have the problem: According to the property we should be able to find the answer this way: We know that and Which gives us the same answer.

FHSPolynomials3 Multiplying Monomials Unlike adding and subtracting, you can multiply any two monomials, even if they are not like terms. Simply multiply the coefficients together, and add the exponents of each set of different variables. Examples: (4 x 2 )( - 5 x 4 ) = (2 x 2 y )(3 x 4 y 2 ) = - 20 x 6 6 x 6 y 3 (4 2 )(4 4 ) = ( x 2 )( x 4 y 5 ) = 4 6 x 6 y 5

FHSPolynomials4 Multiplying a Polynomial by a Monomial To multiply a polynomial by a monomial, you must multiply each term in the polynomial by the monomial. For example: 1. 4(q – 5) multiply both q and 5 by the 4 4 · q – 4 · 5 = 2. (–5x)(5x – 4) = 3. (–3p 2 )(11p 2 + 6pq + 12q 2 ) = 4q – 20 – 25x x –33p 4 – 18p 3 q – 36p 2 q 2

FHSPolynomials5 Problems from WS