Use the Distributive Property to find (5s + 6)(s - 2).
Understand the Problem
The question asks us to use the distributive property to expand and simplify the expression (5s + 6)(s - 2). We need to multiply each term in the first parenthesis by each term in the second parenthesis and then combine like terms to get the final expression.
Answer
$5s^2 - 4s - 12$
Answer for screen readers
$5s^2 - 4s - 12$
Steps to Solve
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Apply the distributive property (FOIL method) Multiply the first terms, the outer terms, the inner terms, and the last terms: $$ (5s + 6)(s - 2) = (5s \cdot s) + (5s \cdot -2) + (6 \cdot s) + (6 \cdot -2) $$
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Perform the multiplications $$ = 5s^2 - 10s + 6s - 12 $$
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Combine like terms Combine the terms with 's': $$ = 5s^2 + (-10s + 6s) - 12 $$ $$ = 5s^2 - 4s - 12 $$
$5s^2 - 4s - 12$
More Information
The distributive property is a fundamental concept in algebra, allowing us to expand expressions and simplify them by combining like terms.
Tips
A common mistake is incorrectly multiplying the terms or making sign errors, especially when dealing with negative numbers. For example, forgetting the negative sign when multiplying $5s$ by $-2$. Another common mistake is not combining like terms correctly. To avoid these mistakes, write out each step carefully and double-check your work.
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