Multiplying Special Case Polynomials – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Are you getting tripped up and slowed down by using the FOIL and area model methods to factor and find the products of polynomials? When working with polynomials, it’s important to keep an eye out for patterns that can help you solve problems quickly and accurately. Watch this video, and you just might learn some new tricks to help you work with special case polynomials.

For the square of a binomial sum, be aware the product is a perfect square trinomial: (a+b)(a+b) = a² + 2ab + b². For the square of a binomial difference, the product is another perfect square trinomial: (a-b)(a-b) = a² -2ab + b². Notice when the terms in the binomials are added, the middle term in the product is positive, and when the terms in the binomials are subtracted, the middle term in the product is negative. The product of a binomial sum and a binomial difference is the difference of two squares or a DOTS: (a+b)(a-b) = a² – b². To identify a DOTS, look for perfect squares.

Watching out for patterns can help you work with polynomials. If you can learn to recognize these three patterns, you can work smart rather than working so darn hard.

Understand the relationship between zeros and factors of polynomials.


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Exercises in this Practice Problem
Calculate the term ${(a+b)^2}$.
Summarize the multiplication of special binomials.
Use the area model to simplify the expression.
Explain the FOIL method to Jack.
Explain the FOIL method.
Simplify the following expressions.