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Chapter 0: Problem 95

Simplify each algebraic expression. $$18 x^{2}+4-\left[6\left(x^{2}-2\right)+5\right]$$

Short Answer

Expert verified
The simplified form of the given algebraic expression is \(12x^{2}+11\).

Step by step solution

01

Distribute multiplication over addition inside the square brackets

The expression inside the square brackets is \(6\left(x^{2}-2\right) + 5\). Distribute 6 in the term \(6\left(x^{2}-2\right)\) to get \(6x^2-12\). So, the entire expression in the square brackets simplifies to \(6x^{2}-12+5 = 6x^{2}-7\). The given expression now simplifies to: \(18x^{2}+4-\left(6x^{2}-7\right)\).
02

Remove brackets

Rewrite the expression by changing the sign of the terms inside the brackets and remove the brackets, which gives: \(18x^{2}+4-6x^{2}+7\).
03

Combine like terms

Rearrange the expression to group like terms together. This gives: \(18x^{2}-6x^{2}+4+7\). Combine the like terms: \(12x^{2}+11\).
04

Simplify

Apart from writing it with the highest degree term first, the terms cannot simplify any further. Thus, the simplified form of the given expression is \(12x^{2}+11\).

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{3}}=-2$$

This will help you prepare for the material covered in the next section. a. Find \(\sqrt{16} \cdot \sqrt{4}\) b. Find \(\sqrt{16 \cdot 4}\) c. Based on your answers to parts (a) and (b), what can you conclude?

Determine whether each statement in Exercises 43鈥�50 is true or false. $$0 \geq-13$$

This will help you prepare for the material covered in the next section. a. Use a calculator to approximate \(\sqrt{300}\) to two decimal places. b. Use a calculator to approximate \(10 \sqrt{3}\) to two decimal places. c. Based on your answers to parts (a) and (b), what can you conclude?

$$\text { Factor completely.}$$ $$6 x^{4}+35 x^{2}-6$$
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