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Question

Multiply:
$$(7x^2 + 12xy - 9y^2) \ by \ (3x^2 - 5xy+ 3y^2)$$

Solution
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$$(7x^2 + 12xy - 9y^2) \times (3x^2 - 5xy+ 3y^2)$$
$$ = 7x^2 (3x^2 - 5xy + 3y^2) + 12xy (3x^2 - 5xy + 3y^2) - 9y^2(3x^2 - 5xy + 3y^2)$$
$$ = 21 x^4 - 35x^3y + 21x^2y^2 + 36x^3y - 60 x^2y^2 + 36 xy^3 - 27 x^2y^2 + 45 xy^3 - 27y^4$$
$$ = 21 x^4 - x^3y + 81xy^3 - 66x^2y^2 - 27y^4$$

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