Problem 95 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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: \(18x^{2}+4-\left(6x^{2}-7\right)\).

Step 2: Remove brackets

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

Step 3: Combine like terms

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

Step 4: 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 \(12x^{2}+11\).