Question

Write in expanded form, (x-2y-3z)^2 & (-2x+5y-3z)^2

Answer 1

1.)

( x - 2y- 3z)^2

= (x)^2 + (-2y)^2 + (-3z)^2 + 2(x)(-2y) +2(-2y)(-3z) +2(-3z)(x)

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

2.)

( - 2x + 5y - 3z)^2

= (-2x)^2 +(5y)^2 + (-3z)^2 + 2(-2x)(5y) + 2(5y)(-3z) + 2(-3z) (-2x)

= 4x^2 + 25y^2 + 9x^2 - 20xy - 30yz + 12zx

Answer 2

Given: Here we have given $(x-2y-3z)^2$ & $(-2x+5y-3z)^2$

To find: Here we have to write in expanded form

Solution:

Here we will expand the first equation

$( x - 2y- 3z)^2 \\= (x)^2 + (-2y)^2 + (-3z)^2 + 2(x)(-2y) +2(-2y)(-3z) +2(-3z)(x) \\= x^2 + 4y^2 + 9z^2 - 4xy + 12yz - 6zx$

Here is the second equation

$( - 2x + 5y - 3z)^2 \\= (-2x)^2 +(5y)^2 + (-3z)^2 + 2(-2x)(5y) + 2(5y)(-3z) + 2(-3z) (-2x) \\= 4x^2 + 25y^2 + 9x^2 - 20xy - 30yz + 12zx$

Final answer:

Hence the answers are $x^2 + 4y^2 + 9z^2 - 4xy + 12yz - 6zx$ and$4x^2 + 25y^2 + 9x^2 - 20xy - 30yz + 12zx$