Question

Subtract. $$ \left(2 x^{2}+3 x-9\right)-(-4 x+7) $$

   Subtract.
$$
\left(2 x^{2}+3 x-9\right)-(-4 x+7)
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 5, Problem 23

Instant Answer

Solved by Expert Emily Himsel

02/07/2022

Step 1

This changes the sign of each term inside the parentheses. So, we have: $$ (2x^{2}+3x-9)-(-4x+7) = 2x^{2}+3x-9+4x-7 $$ Show more…

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Subtract. $$ \left(2 x^{2}+3 x-9\right)-(-4 x+7) $$

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Key Concepts

Combining Like Terms

After distributing the negative sign, like terms—those with the same variable part—are combined by adding or subtracting their coefficients. This process simplifies the expression to its neatest form, reducing complexity and making further algebraic manipulation easier.

Subtraction of Polynomials

Subtracting polynomials involves removing one polynomial from another. This operation requires aligning and properly handling each term by subtracting the coefficients of like powers of the variable. In the process, each term in the polynomial being subtracted is affected, ensuring proper combination of corresponding terms.

Distribution of the Negative Sign

When subtracting a group of terms enclosed in parentheses, the negative sign must be distributed to each term inside the parentheses. This means that every term in the subtracted expression has its sign changed, a critical step to avoid mistakes in subsequent operations.

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