Multiply:$9x^2 + 25y^2 + 15xy + 12x - 20y + 16$ by $3x - 5y + 4$

Given:

$9x^2 + 25y^2 + 15xy + 12x - 20y + 16$ and $3x  - 5y + 4$

To do:

We have to multiply the given expressions.

Solution:

We know that,

$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$

Therefore,

$(9x^2 + 25y^3 + 15xy + 12x - 20y + 16) \times (3x - 5y + 4) = (3x -5y + 4) [(3x)^2 + (-5y)^2 + (4)^2 - 3x \times (-5y) - (-5y \times 4) - (4 \times 3x)]$

$= (3x)^3 + (-5y)^3 + (4)^3 - 3 \times 3x \times (-5y) \times 4$

$= 27x^3 - 125y^3 + 64 + 180xy$

Hence, $(9x^2 + 25y^3 + 15xy + 12x - 20y + 16) \times (3x - 5y + 4) = 27x^3 - 125y^3 + 64 + 180xy$.

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Updated on: 10-Oct-2022

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