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Multiply: x^{2}^{ }+ 4y^{2} + 2*xy* − 3*x* + 6*y* + 9 by* x* − 2*y* + 3

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#### Solution

The given expression is

`x^2 +4y^2 +2xy -3x +6y+9`

We have to multiply the above expression by (x - 2y +3).

The required product is

`(x-2y+3)(x^2 +4y^2 +2xy - 3x +6y +9)`

` = {x+(-2y)+3}{(x)^2 + (-2y)^2 +(3)^2 -x.(-2y) -(-2y).(3) - (3).x}`

Recall the formula

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

Using the above formula, we have

` = x^3 +(-2y)^3 + (3)^3 - 3.x.(-2y).(3)`

` = x^3 -8y^3 +27 +18xy`

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