Question
Simplify the following expressions fully. HW? 1.1.1. \( \quad(x-3)(x+4) \)
Ask by Horton Fernandez. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^2 + x - 12 \)
Solution
1. Expand using the distributive property:
\[
(x-3)(x+4)=x(x+4)-3(x+4)
\]
2. Multiply:
\[
x(x+4)=x^2+4x\quad \text{and}\quad -3(x+4)=-3x-12
\]
3. Combine like terms:
\[
x^2+4x-3x-12=x^2+x-12
\]
The simplified expression is:
\[
x^2+x-12
\]
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Simplify this solution The Deep Dive
To simplify the expression \( (x - 3)(x + 4) \), you can use the distributive property (also known as the FOIL method for binomials). First, multiply the first terms: \( x \times x = x^2 \). Next, multiply the outer terms: \( x \times 4 = 4x \). Then, multiply the inner terms: \( -3 \times x = -3x \). Lastly, multiply the last terms: \( -3 \times 4 = -12 \). Now, combine all these results together: \[ x^2 + 4x - 3x - 12 \] Combine like terms: \[ x^2 + (4x - 3x) - 12 \] So, \( x^2 + 1x - 12 \), or simply \( x^2 + x - 12 \) is your final answer! Happy simplifying!
