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Chapter 10: Problem 509

Add or subtract the polynomials. $$\left(5 u^{2}+8 u\right)-(4 u-7)$$

Short Answer

Expert verified
5u^2 + 4u + 7

Step by step solution

01

Distribute the subtraction

Apply the subtraction by distributing the negative sign to each term in the second polynomial. This means changing the signs of each term in \(4u - 7\). Thus, \( (5u^2 + 8u) - (4u - 7) = 5u^2 + 8u - 4u + 7 \).
02

Combine like terms

Group the like terms together: \(5u^2 + 8u - 4u + 7\). Combine the \(u\) terms by subtracting \(4u\) from \(8u\), which gives \(8u - 4u = 4u\). Now the expression is \(5u^2 + 4u + 7\).
03

Simplify the polynomial

After combining the like terms, the simplified polynomial expression is \(5u^2 + 4u + 7\).

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Key Concepts

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

Distribute the subtraction
To distribute the subtraction, you need to apply the negative sign to each term in the second polynomial. This changes their signs.
In our example, the polynomials are the first one: the second one: to perform the subtraction, distribute the sign like this: Thus, transforms into . By changing the signs, the expression transforms into .
Combine like terms
Combining like terms means grouping and then simplifying terms that have the same variables and powers. In our example, we have the expression First, identify the like terms in the given expression:
  • is a constant or a term with zero power.
  • are terms with the variable .
  • remains as it is, as there are no other -squared terms.
Now, sum the coefficients of the like terms:
The terms combining results in , and the term remains unchanged..
Simplify polynomial
Simplifying the polynomial involves combining all the like terms into their simplest form. The expression we simplified is Combining like terms, we get the final simplified polynomial is

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