Question
multiply. \( -4 x y^{2}\left(3 x^{2}+5 x y^{2}-8 x y\right) \)
Ask by Tyler Schofield. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Multiply \( -4 x y^{2}\left(3 x^{2}+5 x y^{2}-8 x y\right) \) to get \( -12x^{3}y^{2}-20y^{4}x^{2}+32y^{3}x^{2} \).
Solution
Calculate or simplify the expression \( -4*x*y^2*(3*x^2+5*x*y^2-8*x*y) \).
Simplify the expression by following steps:
- step0: Solution:
\(-4xy^{2}\left(3x^{2}+5xy^{2}-8xy\right)\)
- step1: Rewrite the expression:
\(-4\left(3x^{2}+5xy^{2}-8xy\right)xy^{2}\)
- step2: Multiply the expression:
\(-4\left(3x+5y^{2}-8y\right)x^{2}y^{2}\)
- step3: Rearrange the terms:
\(-12x^{3}y^{2}-20y^{4}x^{2}+32y^{3}x^{2}\)
The result of multiplying \( -4 x y^{2}\left(3 x^{2}+5 x y^{2}-8 x y\right) \) is \( -12x^{3}y^{2}-20y^{4}x^{2}+32y^{3}x^{2} \).
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Simplify this solution Mind Expander
When you multiply \( -4xy^{2} \) by each term in the polynomial \( (3x^{2} + 5xy^{2} - 8xy) \), you distribute \( -4xy^{2} \) to each term: 1. \( -4xy^{2} \cdot 3x^{2} = -12x^{3}y^{2} \) 2. \( -4xy^{2} \cdot 5xy^{2} = -20x y^{4} \) 3. \( -4xy^{2} \cdot (-8xy) = 32x^{2}y^{3} \) Now, combine all the terms together: \[ -12x^{3}y^{2} - 20xy^{4} + 32x^{2}y^{3} \] So, the final result of multiplying \( -4xy^{2}(3x^{2}+5xy^{2}-8xy) \) is: \[ -12x^{3}y^{2} + 32x^{2}y^{3} - 20xy^{4} \]
