Question

expand (2x+3y+4z)^2​

Answer 1

Given :-

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

To ,

Expand the above expression

Solution :-

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

$\sf {4x}^{2} + {9y}^{2} + {16z}^{2} + 12xy + 24yz + 16zx$

Procedure :-

→ This question is from Algebraic identites.

→ In total their are 10 algerbric identites, and this question is going to be solved by using 5th algerbric identity, which is (a+b+c)² = a² + b² + c² +2ab + 2bc + 2ca.

→ First we will do square of 2x, 3y and 4z then we will first multiply the constants given in brackets and then we will multiply it with the 2 which is outside the bracket.

Other Identities :-

$\sf {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

$\sf {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

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

$\sf (x + a)(x + b) = {x}^{2} + (a + b)x + (a \times b)$

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