Question

25. The expanded form of (x + y - z)2 is​

Answer 1

Step-by-step explanation:

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Answer 2

AnsweR :-

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

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

$\sf {x}^{2} + {y}^{2} - {z}^{2} +2xy - 2yz - 2zx$

Procedure :-

→ This is the 5th identity of Algerbric identites in maths. The 5th Indentity says (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2zx.

→ For understanding this identity let's take an example :-

(2x + 3y + 4z)² = (2x)²+ (3y)²+ (4x)²+ 2(2x)(3y) + 2(3y)(4z) + 2(4z) + (2x)

→ 4x² + 9y² + 16z² + 12xy + 24yz + 16zx

→ But according to your question z is negetive because of that the other signs will get affected. First we will multiply the constants in the brackets and then we will multiply it with the 2 which is outside the bracket.

→ If z is negetive then the positive sign will change into negetive sign because (+)(-) = -

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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