Multiply:$x^2 + 4y^2 + 2xy - 3x + 6y + 9$ by $x - 2y + 3$

Given:

$x^2 + 4y^2 + 2xy - 3x + 6y + 9$ and $x - 2y + 3$

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,

$(x^2 + 4y^2 + 2xy - 3x + 6y + 9) \times (x - 2y + 3) = (x - 2y + 3) (x^2 + 4y^2 + 9 + 2xy + 6y - 3x)$

$= (x)^3 + (-2y)^3 + (3)^3 - 3 \times x \times (-2y) \times 3$

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

Hence, $(x^2 + 4y^2 + 2xy - 3x + 6y + 9) \times (x - 2y + 3) = x^3 - 8y^3 + 27 + 18xy$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

40 Views

Kickstart Your Career

Get certified by completing the course

Get Started