Question

Use the distributive property and mental math to simplify the expression. $$ 8 t^{2}-2 t+5 t-4 $$

Short answer

The simplified form of the algebraic expression is \(8 t^{2} + 3t - 4\).

Step-by-step solution

Identify Like Terms

In this given expression \(8 t^{2}-2 t+5 t-4\), the like terms are \(-2t\) and \(+5t\) as they both have the variable \(t\) to the power of 1.

Combine Like Terms

Now, combine these like terms by adding or subtracting their coefficients. Here, \(-2t + 5t\) becomes \(3t\). This will give us the new expression: \(8 t^{2} + 3t - 4\).

Final simplified expression

So after combining like terms, the simplified algebraic expression is \(8 t^{2} + 3t - 4\).