Question

Multiply the binomials. $$\left(x^{2}-2\right)\left(x^{2}+4\right)$$

   Multiply the binomials.
$$\left(x^{2}-2\right)\left(x^{2}+4\right)$$

College Algebra with Modeling and Visualization

College Algebra with Modeling and Visualization

Gary K. Rockswold 4th Edition

Chapter 0, Problem 64

Instant Answer

Solved by Expert Julie Silva

04/14/2021

Step 1

This gives us: $$x^{2} \cdot x^{2} + x^{2} \cdot 4 - 2 \cdot x^{2} - 2 \cdot 4$$ Show more…

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Multiply the binomials. $$\left(x^{2}-2\right)\left(x^{2}+4\right)$$

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Key Concepts

Polynomial Multiplication

Polynomial multiplication involves multiplying two polynomials together to obtain another polynomial. This process requires applying the distributive property to multiply every term in the first polynomial by every term in the second polynomial, and then combining any like terms to simplify the expression.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. It is used in polynomial multiplication to ensure that every term in one polynomial is properly multiplied by every term in another polynomial, facilitating the expansion and simplification of the overall expression.

Combining Like Terms

Combining like terms is the process of simplifying an algebraic expression by merging terms that have the same variables raised to the same powers. After all terms have been generated through multiplication, like terms are summed up to simplify and condense the expression into its simplest form.

Binomials

A binomial is a polynomial that consists of exactly two terms. Multiplying binomials is a specific application of polynomial multiplication, often using strategies like the FOIL method, which stands for First, Outer, Inner, Last, to systematically perform the multiplication.

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