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Chapter 5: Problem 71

Subtract. $$ \begin{array}{r}{6 m^{2}-11 m+5} \\ {-8 m^{2}+2 m-1} \\ \hline\end{array} $$

Short Answer

Expert verified
14m^2 - 13m + 6

Step by step solution

01

Write Down the Problem

Write down the given polynomials that need to be subtracted: \[ 6m^2 - 11m + 5 \] \[ -8m^2 + 2m - 1 \]
02

Change the Signs of the Second Polynomial

The operation is subtraction, so change the signs of each term of the second polynomial: \[ -8m^2 + 2m - 1 \] becomes \[ 8m^2 - 2m + 1 \]
03

Combine Like Terms

Add the polynomials together by combining like terms: \[ (6m^2 + 8m^2) + (-11m - 2m) + (5 + 1) \] Which simplifies to \[ 14m^2 - 13m + 6 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

like terms
In algebra, 'like terms' are terms that have exactly the same variables raised to the same powers. The coefficients may differ, but the variable part must be identical.

For example, in the polynomials provided in the exercise, the following are like terms:
  • sup>2
recognizing like terms allows us to combine them efficiently.

Consider sub>2. Both terms have the variable mevery term separately.
combining polynomials
Combining polynomials is a method to simplify expressions by adding or subtracting them. This process often involves combining like terms.

In the given exercise:
  • We write down the polynomials: (8m^2 mess)
polyno is the combination

    6m^2 original polynom
parating it all
4ms withra1 order:<8m

sion thering1 )&2;)<4m^ }
changing signs
Changing signs is essential in polynomial subtraction because we need to 'distribute' the minus sign across all terms of the polynomial being subtracted. In other words, we change each term鈥檚 sign from positive to negative, and from negative to positive.
br>In the exercise:
  • We have the second polynomial: = changingts changes:
becomes: losses

This ensures polynomialssubtra< fromalul term properly.vale3

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Most popular questions from this chapter

In Exercises 65鈥�74, the factors involve fractions or decimals. Apply the methods of this sec- tion, and find each product. $$ \left(3 w+\frac{1}{4} z\right)(w-2 z) $$

Find each product. $$ \left(m^{2}-2 m p+p^{2}\right)\left(m^{2}+2 m p-p^{2}\right) $$

Simplify each expression. $$ 9 x+5 x-x+8 x-12 x $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \left(k^{2}\right)^{-3} k^{4} $$

Two expressions are given. Replace x with 3 and y with 4 to show that, in general, the two expressions are not equivalent. $$ (x+y)^{4} ; \quad x^{4}+y^{4} $$
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