Question
Multiply and collect the like terms \[ (5 x-3 y) \cdot(4 x+7 y-1) \] Provide your answer below:
Ask by Gonzalez Stewart. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(20x^2 + 23xy - 5x - 21y^2 + 3y\).
Solution
1. Distribute each term of the first parentheses over the terms of the second parentheses:
\[
(5x - 3y)(4x + 7y - 1) = 5x(4x) + 5x(7y) + 5x(-1) - 3y(4x) - 3y(7y) - 3y(-1)
\]
2. Compute the individual products:
\[
5x(4x) = 20x^2,\quad 5x(7y) = 35xy,\quad 5x(-1) = -5x,
\]
\[
-3y(4x) = -12xy,\quad -3y(7y) = -21y^2,\quad -3y(-1) = 3y.
\]
3. Combine these results:
\[
20x^2 + 35xy - 5x - 12xy - 21y^2 + 3y.
\]
4. Combine like terms (specifically the \(xy\) terms):
\[
35xy - 12xy = 23xy.
\]
5. The simplified expression is:
\[
20x^2 + 23xy - 5x - 21y^2 + 3y.
\]
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Simplify this solution Extra Insights
To solve the expression \( (5x - 3y) \cdot (4x + 7y - 1) \), we will utilize the distributive property (also known as the FOIL method). 1. Distribute \( 5x \): - \( 5x \cdot 4x = 20x^2 \) - \( 5x \cdot 7y = 35xy \) - \( 5x \cdot (-1) = -5x \) 2. Distribute \( -3y \): - \( -3y \cdot 4x = -12xy \) - \( -3y \cdot 7y = -21y^2 \) - \( -3y \cdot (-1) = 3y \) Now, we combine all these results: \[ 20x^2 + 35xy - 5x - 12xy - 21y^2 + 3y \] Next, we collect like terms: - For the \(xy\) terms: \( 35xy - 12xy = 23xy \) The final answer, after collecting like terms, is: \[ 20x^2 + 23xy - 5x - 21y^2 + 3y \]
