Jeanine08181977idn
Answered

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What is the factored form of [tex]$x^2 y^3 - 2 y^3 - 2 x^2 + 4$[/tex]?

[tex]\[
\begin{array}{c}
\left(x^2 y^3 + 4\right) - 2\left(y^3 + x^2\right) \\
\left(x^2 - 2\right)\left(y^3 - 2\right) \\
y^3\left(x^2 - 2\right) + 2\left(-x^2 + 2\right)
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To find the factored form of the polynomial [tex]\( x^2 y^3 - 2 y^3 - 2 x^2 + 4 \)[/tex], let's break down the polynomial and look for common factors or group terms. Follow these steps:

1. Identify the polynomial:
[tex]\[ x^2 y^3 - 2 y^3 - 2 x^2 + 4 \][/tex]

2. Group the terms to look for common factors:
[tex]\[ (x^2 y^3 - 2 x^2) + (-2 y^3 + 4) \][/tex]

3. Factor out common terms within each group:
[tex]\[ x^2(y^3 - 2) - 2(y^3 - 2) \][/tex]

4. Notice that [tex]\( (y^3 - 2) \)[/tex] is a common factor in both groups:
[tex]\[ (y^3 - 2)(x^2 - 2) \][/tex]

So, the factored form of the polynomial [tex]\( x^2 y^3 - 2 y^3 - 2 x^2 + 4 \)[/tex] is:
[tex]\[ (x^2 - 2)(y^3 - 2) \][/tex]

To summarize, the polynomial [tex]\( x^2 y^3 - 2 y^3 - 2 x^2 + 4 \)[/tex] factors into [tex]\( (x^2 - 2)(y^3 - 2) \)[/tex].
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