Multiplying Polynomials – Practice Problems

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Multiplying polynomials combines the laws of exponents for multiplication and adding polynomials. To multiply two polynomials, we use the distributive property, [a(b +c + d) = ab + ac + ad], to make sure that each term of one polynomial is multiplied with every term of the other. Then, we add the results by combining like terms. There are different situations to consider:

(1) Multiplication of a Monomial by another Monomial
e.g. (5xy)(-2y) = -10xy²

(2) Multiplication of a Monomial by a Polynomial
e.g. (-3x)(2x² - 5x + 1) = (-3x)(2x²) + (-3x)(-5x) + (-3x)(1) = -6x³ + 15x² - 3x

(3) Multiplication of a Polynomial by another Polynomial
e.g. (x + 5)(-x² + 8x - 3) = (x)(-x²) + (x)(8x) + (x)(-3) + 5(-x²) + 5(8x) + 5(-3)
= -x³ + 8x² - 3x - 5x² + 40x - 15
= -x³ + 3x² + 37x - 15

For example, let's say that the length of a rectangular window is 5 feet more than its width, w². With this information we can write an algebraic expression for the area of the window: we have that its width = w² and its length = w² + 5. So the area of the rectangular window = w²(w² + 5) = w⁴ + 5w².

Perform arithmetic operations on polynomials.

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Exercises in this Practice Problem
Multiply two binomials using the FOIL method.
Determine the area of Rap-Punzel's closet.
Calculate the area of the bed using the area model.
Check the area model for the given products.
Decide which statements are true about the FOIL method.
Solve the following products.