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RRB ALP CBT I 25 Nov 2024 Shift 2 Paper

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Question : 22 of 75

Marks: +1, -0

Simplify the following expression:

(2z-5y)^{2}+(5z+2y)^{2}-25z^{2}

19y²+4z²
19y²-4z²
29y²+4z²
29y²-4z²

Solution:

Concept:

Use standard algebraic identities for squares of binomials.

Explanation:

Expand each squared term using the identities

(a-b)^2 = a^2 - 2ab + b^2

and

(a+b)^2 = a^2 + 2ab + b^2

.

(2z-5y)^2 = 4z^2 - 20zy + 25y^2

(5z+2y)^2 = 25z^2 + 20zy + 4y^2

Adding these gives:

4z^2 - 20zy + 25y^2 + 25z^2 + 20zy + 4y^2

The

zy

terms cancel, so we get:

29z^2 + 29y^2

Now subtract

25z^2

from this result:

29z^2 + 29y^2 - 25z^2 = 4z^2 + 29y^2

Rearranging gives

29y^2 + 4z^2

.

Answer:

29y^2 + 4z^2

Option C.

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