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Chapter 0: Problem 96

Simplify each algebraic expression. $$14 x^{2}+5-\left[7\left(x^{2}-2\right)+4\right]$$

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(7x^{2}+15\)

Step by step solution

01

Distribute the Outside Term

Distribute the outside term to each term in the parenthesis. In this case, distribute 7 to each term inside the parenthesis.\nSo the given expression \(14x^{2}+5-[7(x^{2}-2)+4]\) becomes: \(14x^{2}+5-(7x^{2}-14+4)\)
02

Simplify Inside the Parentheses

Combine the constants inside the parentheses \nSo \(14x^{2}+5-(7x^{2}-14+4)\) simplifies to : \(14x^{2}+5-(7x^{2}-10)\)
03

Simplify Outside the Parentheses

Apply the minus sign in front of the parentheses to all elements inside it. So \(14x^{2}+5-(7x^{2}-10)\) simplifies to : \(14x^{2}+5-7x^{2}+10\)
04

Combine Like Terms

Finally, combine like terms. The like terms in the given problem are \(14x^{2}+5-7x^{2}+10\) , which when combined gives : \(7x^{2}+15\)

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Most popular questions from this chapter

Explain how to add \(\sqrt{3}+\sqrt{12}\)

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right)$$

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