Problem 96 - Algebra and Trigonometry

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 given algebraic expression is \(7x^{2}+15\)

Step 1: 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: \(14x^{2}+5-(7x^{2}-14+4)\)

Step 2: Simplify Inside the Parentheses

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

Step 3: 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 : \(14x^{2}+5-7x^{2}+10\)

Step 4: 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 : \(7x^{2}+15\)