Question

expand using identities (2x-3y+5z)2

Answer 1

given :- ( 2x - 3y + 5z )²


by using identity ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac

here a = 2x, b = -3y and c = 5z

now let us solve it..

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

= 4x² + 9y² + 25z² - 12xy - 30yz + 20xz

HOPE THIS HELPS..!!

Answer 2

Answer:

After expansion answer is $4 {x}^{2} + 9 {y}^{2} + 25 {z}^{2} + 20xz - 30yz - 12xy$

Step-by-step explanation:

Given,

${(2x - 3y + 5z)}^{2}$

We are comparing it with

${(a + b)}^{2}$

So,

$a = 2x - 3y \\ b = 5z$

We know,

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

So,

${(2x - 3y + 5z)}^{2} \\= {(2x - 3y)}^{2} + 2.(2x - 3y).5z + {(5z)}^{2}$

$\\ = {(2x)}^{2} - 2.2x.3y + {(3y)}^{2}+ 20xz - 30yz + 25 {z}^{2}$ $= 4 {x}^{2} + 9 {y}^{2} - 12xy + 20xz - 30yz + 25 {z}^{2}$

$= 4 {x}^{2} + 9 {y}^{2} + 25 {z}^{2} + 20xz - 30yz - 12xy$

This is a problem of Algebra,

Some important formulas of Algebra,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

${a}^{2} - {b}^{2} = (a + b)(a - b)\\{a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab\\{a}^{2} + {b}^{2} = {(a - b)}^{2} + 2ab\\{a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )\\{a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$