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Chapter 6: Problem 65

Simplify each algebraic expression. \(2\left(3 x^{2}-5\right)-\left[4\left(2 x^{2}-1\right)+3\right]\)

Short Answer

Expert verified
\(-2x^{2} - 9\)

Step by step solution

01

Distribute Multiplication Across Parenthesis

Use the distributive property to remove the parentheses. That is, multiply each term inside the parentheses by the term just before it on the outside. \(2 \cdot (3x^{2}-5)\) becomes \(6x^{2} - 10\), and \(4 \cdot (2x^{2}-1)\) becomes \(8x^{2} - 4\).
02

Simplify Inside The Bracket

As per the order of operations, calculate the expression inside the bracket first. Then perform the subtraction. So, \(8x^{2} - 4 + 3\) simplifies to \(8x^{2} - 1\).
03

Subtract The Two Expressions

Now, subtract the expression obtained in Step 2 from the expression obtained in Step 1: \(6x^{2} - 10 - (8x^{2} - 1)\). The minus sign before the parentheses serves to change the sign of each term inside the parentheses. This gets us \(-2x^{2} - 9\).
04

Combine Like Terms

The expression obtained in Step 3, \(-2x^{2} - 9\), cannot be further simplified as there are no like terms to combine. Hence, this will be the final simplified form of the original expression.

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-14 x+45\)

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In Exercises 33-36, solve each equation using the zero-product principle. \(x^{2}+8 x+15=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(2 x^{2}+7 x+3\)

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