Question
14. \( (2 x y)^{2}\left(-3 x^{2}\right)\left(4 y^{2}\right) \)
Ask by Ruiz Malone. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form is \(-48x^4y^4\).
Solution
Calculate or simplify the expression \( (2*x*y)^2*(-3*x^2)*(4*y^2) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2xy\right)^{2}\left(-3x^{2}\right)\times 4y^{2}\)
- step1: Rewrite the expression:
\(-\left(2xy\right)^{2}\times 3x^{2}\times 4y^{2}\)
- step2: Multiply the terms:
\(-\left(2xy\right)^{2}\times 12x^{2}y^{2}\)
- step3: Multiply the terms:
\(-48x^{4}y^{4}\)
The simplified form of the expression \( (2xy)^2(-3x^2)(4y^2) \) is \(-48x^4y^4\).
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Simplify this solution The Deep Dive
To simplify \( (2xy)^{2}(-3x^{2})(4y^{2}) \), we begin by breaking it down. First, calculate \( (2xy)^{2} \) which gives us \( 4x^{2}y^{2} \). Now, we can multiply this by the other terms: \( 4x^{2}y^{2} \cdot (-3x^{2}) \cdot (4y^{2}) \). Now, let's multiply the constants: \( 4 \cdot (-3) \cdot 4 = -48 \). Then, combine the \( x \) and \( y \) terms: \( x^{2} \cdot x^{2} = x^{4} \) and \( y^{2} \cdot y^{2} = y^{4} \). Putting it all together, we get \( -48x^{4}y^{4} \). So, the simplified expression is: \[ -48x^{4}y^{4} \]
