Products of polynomials
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers multiplying polynomials together to form products of polynomials. Students extend the distributive property to multiply binomials by trinomials and larger polynomials, combining like terms in the result to produce a fully simplified polynomial.
Key Concepts
Property To find the product of two polynomials, multiply each term of the first polynomial by each term of the second polynomial, then combine any like terms.
If a product contains a monomial factor, it is a good idea to multiply the polynomial factors together first, and save the monomial factor for last.
Examples To multiply $(x+5)(2x^2 x 3)$, we distribute term by term: $x(2x^2 x 3) + 5(2x^2 x 3) = 2x^3 x^2 3x+10x^2 5x 15 = 2x^3+9x^2 8x 15$.
Common Questions
How do you multiply two polynomials?
Distribute every term of the first polynomial by every term of the second, then combine like terms in the resulting sum.
What is the FOIL method?
FOIL stands for First, Outer, Inner, Last. It is a systematic way to multiply two binomials by multiplying each pair of terms and adding the results.
How do you multiply a binomial by a trinomial?
Distribute each term of the binomial to all three terms of the trinomial, producing 6 terms, then combine any like terms.
What is an example of a product of polynomials?
(x+2)(x^2+3x+1) = x^3+3x^2+x+2x^2+6x+2 = x^3+5x^2+7x+2 after combining like terms.
Where are products of polynomials taught?
Products of polynomials are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.