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Simplify the expression:

[tex]\[ \left(9 - x^2\right)\left(100 - y^2\right) - 120xy \][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's work through the expression step-by-step:

Given the expression:
[tex]\[ (9 - x^2)(100 - y^2) - 120xy \][/tex]

Step 1: First, expand the product [tex]\((9 - x^2)(100 - y^2)\)[/tex].

Start by using the distributive property (FOIL method):
[tex]\[ (9 - x^2)(100 - y^2) = 9 \cdot 100 - 9 \cdot y^2 - x^2 \cdot 100 + x^2 \cdot y^2 \][/tex]

Let's multiply each term:
[tex]\[ 9 \cdot 100 = 900 \][/tex]
[tex]\[ 9 \cdot (-y^2) = -9y^2 \][/tex]
[tex]\[ (-x^2) \cdot 100 = -100x^2 \][/tex]
[tex]\[ (-x^2) \cdot (-y^2) = x^2 y^2 \][/tex]

Combining all these results:
[tex]\[ 900 - 9y^2 - 100x^2 + x^2 y^2 \][/tex]

Step 2: Now subtract the [tex]\(120xy\)[/tex] term from the expanded expression:
[tex]\[ 900 - 9y^2 - 100x^2 + x^2 y^2 - 120xy \][/tex]

Therefore, the final expanded form of the expression [tex]\((9 - x^2)(100 - y^2) - 120xy\)[/tex] is:
[tex]\[ x^2 y^2 - 100x^2 - 120xy - 9y^2 + 900 \][/tex]

This is the completely expanded form of the given expression.
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