Question

Simplify: $2(x+h)^{2}+3(x+h)+5-\left(2 x^{2}+3 x+5\right)$

   Simplify: $2(x+h)^{2}+3(x+h)+5-\left(2 x^{2}+3 x+5\right)$

College Algebra Essentials

College Algebra Essentials

Robert Blitzer 4th Edition

Chapter 2, Problem 131

Instant Answer

Solved by Expert Erika Bustos

08/20/2021

Step 1

\[ (x+h)^2 = x^2 + 2xh + h^2 \] Show more…

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Simplify: $2(x+h)^{2}+3(x+h)+5-\left(2 x^{2}+3 x+5\right)$

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Key Concepts

Expansion of Binomials

This concept involves multiplying out expressions like (x + h)^2 to rewrite it as x^2 + 2xh + h^2. Expanding binomials is a fundamental algebraic technique that helps transform expressions into a standard polynomial form, which often makes further manipulation and simplification easier.

Distribution of Multiplication and Subtraction

This involves applying the distributive property to multiply constants with the expanded binomial, as well as carefully distributing the negative sign across the terms of another polynomial. Correctly distributing these factors ensures that the expression is set up correctly for combining like terms.

Combining Like Terms

After expansion and distribution, similar terms (those with the same variable parts) need to be combined to simplify the expression. This process reduces the polynomial to its simplest form by adding or subtracting coefficients of these like terms.

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