Question

(2x-3y + 4z)² give answer​

Answer 1

Question:

Find the value of :-

${(2x - 3y + 4z) }^{2}$

Answer:

(2x−3y+4z)² = 4x² + 9y² + 16z² - 12xy - 24yz +16xz .

Step-by-step explanation:

We know that,

$\boxed{ \sf {(a + b + c) }^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac}$

$\bold{{(2x - 3y + 4z) }^{2} }$

$Here, \: a = 2x, \: b = - 3y, \: c = 4z$

$\sf= {(2x)}^{2} + {( - 3y) }^{2} + {(4z)}^{2} + 2(2x)( - 3y) + 2( - 3y)(4z) + 2(2x)(4z)$

$= \boxed{ \sf4 {x}^{2} + 9 {y}^{2} + 16 {z}^{2} - 12xy - 24yz + 16xz}$

$\therefore$ (2x−3y+4z)² = 4x² + 9y² + 16z² - 12xy - 24yz + 16xz .

Formula used:

$\bigstar {(a + b + c) }^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac$

Formula to know:

$\bigstar {(a+b)}^{2} = a^{2} + 2ab+b^{2}$

$\bigstar {(a-b)}^{2} = a^{2} - 2ab+b^{2}$

$\bigstar (x+a)(x+b)=x^{2}+x(a+b)+ab$