Question

expand the following (x-2y+3z) to the power 2

Answer 1

use identity ,

(a + b+ c )^2 = a^2 + b^2 + 2ab + 2bc + 2ca

here a =x ,b = -2y , c = 3z

(x -2y +3z)^2

= x^2 + 4y^2 +9z^2 - 4xy - 12yz +6zx

hope it helps!

thank you!

Answer 2

Hello!
Here is your answer
$(x - 2y + 3z) {}^{2}$
Let 'x'be 'a'

Let '2y + 3z' be 'b'.
$(a - b) {}^{2} = a {}^{2} - 2ab + b {}^{2}$
Then
$(x - 2y + 3z) {}^{2} = x {}^{2} - 2(x)(2y + 3z) + (2y + 3z) {}^{2}$
Here

2y + 3z is in the form (α+β)

Here α and β are just symbols to represent them.

$( \alpha + \beta ) {}^{2} = \alpha ^{2} + 2 \alpha \beta + \beta {}^{2}$
$(2y + 3z) {}^{2} = (2y) {}^{2} + 2(2y)(3z) + (3z) {}^{2}$
$= 4y {}^{2} + 12yz + 9z {}^{2}$
Therefore for (x - 2y + 3z)
$x {}^{2} - 4yx - 6xz + 4y {}^{2} + 12yz + 9z {}^{2}$
$= x {}^{2} + 4y {}^{2} + 9z {}^{2} - {4xy} - 6xz + 12yz$
This Can be solved using another method Too...

This question is in the form of (a+b+c)^2

Where
a = x
b = -2y
c = 3z
$(a + b + c) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2ab + 2bc + 2ca$
Thank you.......