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CTET Paper II (Mathematics and Science) 4 Jan 2022 Solved Paper

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Question : 39 of 150

Marks: +1, -0

\frac{(x-y+z)^{2}-(x-y-z)^{2}}{4}

is equal to

z(x - y)
x(y - z)
y(z - x)
x(z - y)

Solution:

Concept:

Use the identity

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

to simplify the expression quickly.

Explanation:

Let

a = x - y + z

and

b = x - y - z

.

Then

a - b = (x - y + z) - (x - y - z) = 2z

.

And

a + b = (x - y + z) + (x - y - z) = 2(x - y)

.

Thus,

(x - y + z)^2 - (x - y - z)^2 = (a - b)(a + b) = (2z) \times 2(x - y) = 4z(x - y)

.

Divide by

4

:

\frac{4z(x - y)}{4} = z(x - y)

.

Answer:

A.

z(x - y)

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