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Multiply the binomials.

[tex]\[
\begin{array}{l}
\left(7x^2 - 3y^2\right)\left(x^2 - 8y^2\right) \\
\left(7x^2 - 3y^2\right)\left(x^2 - 8y^2\right) =
\end{array}
\][/tex]

(Simplify your answer.)

Sagot :

GinnyAnswer
Sure, let's multiply the given binomials step by step:

Given binomials:
[tex]\[ (7x^2 - 3y^2)(x^2 - 8y^2) \][/tex]

To simplify, we will use the distributive property, also known as the FOIL method for binomials:

1. First terms: Multiply the first term of each binomial:
[tex]\[ 7x^2 \cdot x^2 = 7x^4 \][/tex]

2. Outer terms: Multiply the outer terms:
[tex]\[ 7x^2 \cdot (-8y^2) = -56x^2y^2 \][/tex]

3. Inner terms: Multiply the inner terms:
[tex]\[ (-3y^2) \cdot x^2 = -3x^2y^2 \][/tex]

4. Last terms: Multiply the last term of each binomial:
[tex]\[ (-3y^2) \cdot (-8y^2) = 24y^4 \][/tex]

Now, add all these products together:
[tex]\[ 7x^4 + (-56x^2y^2) + (-3x^2y^2) + 24y^4 \][/tex]

Combine like terms (the [tex]\(x^2y^2\)[/tex] terms):
[tex]\[ 7x^4 - 56x^2y^2 - 3x^2y^2 + 24y^4 = 7x^4 - 59x^2y^2 + 24y^4 \][/tex]

Therefore, the product of the given binomials is:
[tex]\[ 7x^4 - 59x^2y^2 + 24y^4 \][/tex]
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