Question
Multiply. \[ (b-3)(b+7) \] \( (b-3)(b+7)=\square \) (Simplify your answer.)
Ask by Donnelly Valdez. in the United States
Feb 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (b - 3)(b + 7) = b² + 4b - 21 \)
Solution
To multiply (b - 3)(b + 7), use the distributive property (FOIL method):
b·b = b²
b·7 = 7b
-3·b = -3b
-3·7 = -21
Now, combine like terms:
b² + 7b - 3b - 21 = b² + 4b - 21
So, (b - 3)(b + 7) = b² + 4b - 21.
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Simplify this solution Bonus Knowledge
To multiply the expression \((b-3)(b+7)\), we can use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). First, multiply the first terms: \(b \times b = b^2\). Next, multiply the outside terms: \(b \times 7 = 7b\). Then, multiply the inside terms: \(-3 \times b = -3b\). Finally, multiply the last terms: \(-3 \times 7 = -21\). Now, combine all these results: \[ b^2 + 7b - 3b - 21 = b^2 + (7b - 3b) - 21 = b^2 + 4b - 21. \] Thus, \[ (b-3)(b+7) = b^2 + 4b - 21. \]
