Problem 96 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The simplified form of the expression \(14 x^{2}+5-\left[7\left(x^{2}-2\right)+4\right]\) is \(7x^{2} + 15\).

Step 1: Distribute inside the brackets

First, simplify the expression inside the brackets. Distribute \(7\) into \((x^{2}-2)\). This yields \(14 x^{2}+5-[7x^{2}-14+4]\).

Step 2: Simplify inside the brackets

Next, combine the constants inside the brackets which yields \(14 x^{2}+5-[7x^{2}-10]\).

Step 3: Distribute the negative outside the brackets

The next step is to distribute the negative sign outside the brackets to each term inside the brackets. This yields \(14 x^{2}+5- 7x^{2}+10\).

Step 4: Combine like terms

The final step is to combine like terms. First, combine \(14 x^{2}\) and \(-7x^{2}\) for a total of \(7x^{2}\). Then combine the constants \(5\) and \(10\) for a total of \(15\). This yields the simplified expression: \(7x^{2}+15\)