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प्रश्न
Multiply: x2 + 4y2 + 2xy − 3x + 6y + 9 by x − 2y + 3
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उत्तर
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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