Question

Multiply the binomials. Use any method. $$(x-7)(x-2)$$

   Multiply the binomials. Use any method.
$$(x-7)(x-2)$$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 6, Problem 244

Instant Answer

Solved by Expert Katelyn Vandeaver

07/14/2021

Step 1

This gives us $x \cdot x$ and $x \cdot -2$. \[x \cdot x = x^2\] \[x \cdot -2 = -2x\] Show more…

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Multiply the binomials. Use any method. $$(x-7)(x-2)$$

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Key Concepts

FOIL Method

FOIL is an acronym for First, Outer, Inner, Last, a mnemonic used to remember the order of multiplications when expanding the product of two binomials. This method is essentially an application of the distributive property, highlighting the specific pairs of terms that need to be multiplied together.

Combining Like Terms

After the application of the distributive property or FOIL method, the resulting expression often has terms that are similar, meaning they have the same variable parts and exponents. Combining like terms is the process of simplifying the expression by adding or subtracting these similar terms to arrive at the simplest possible form.

Binomials

Binomials are algebraic expressions that consist of two terms, typically connected by a plus or minus operator. They are a basic unit in algebra used to model linear relationships and are often the building blocks for polynomial expressions.

Distributive Property

The distributive property is a fundamental property of arithmetic and algebra that allows you to multiply a single term by each term within a parenthesis. When multiplying two binomials, this property ensures that each term in the first binomial is multiplied by each term in the second binomial, leading to a complete and correct expansion of the product.

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