Question

Multiply. See Example 6. $$ \left(x^{2}+6 x+7\right)(2 x-5) $$

   Multiply. See Example 6.
$$
\left(x^{2}+6 x+7\right)(2 x-5)
$$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 5, Problem 61

Instant Answer

Solved by Expert Melissa Stefan

03/22/2020

Step 1

This gives us: $2x \cdot x^2 + 2x \cdot 6x + 2x \cdot 7 - 5 \cdot x^2 - 5 \cdot 6x - 5 \cdot 7$. Show more…

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Multiply. See Example 6. $$ \left(x^{2}+6 x+7\right)(2 x-5) $$

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Key Concepts

Distributive Property

This property is a cornerstone of algebra that states a term multiplied by a sum of terms can be distributed across each term in the sum, i.e., a*(b + c) = a*b + a*c. It is extensively used in polynomial multiplication to ensure that every term in one polynomial is multiplied by every term in the other.

Polynomial Multiplication

This concept involves multiplying each term in one polynomial by every term in another polynomial. It is a fundamental process in algebra that allows one to expand and simplify the product of polynomials, leading to another polynomial whose degree is the sum of the degrees of the factors.

Combining Like Terms

After the multiplication of terms using the distributive property, the resulting expression often contains several like terms—terms that have identical variable parts. Combining like terms is the process of simplifying the expression by adding or subtracting these terms, resulting in a more concise polynomial.

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