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WAEC Mathematics 2022 Paper

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Question : 13

Total: 47

If 5x + 3y=4 and 5x-3y= 2, what is the value of (25x

^2

^2

)?

20
16
2
8

Solution:

Concept:

Use the identity

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

with

a = 5x

and

b = 3y

.

Explanation:

Given equations:

5x + 3y = 4

5x - 3y = 2

Notice that:

25x^2 - 9y^2 = (5x)^2 - (3y)^2

So,

25x^2 - 9y^2 = (5x - 3y)(5x + 3y)

.

Substitute the given values directly:

(5x - 3y)(5x + 3y) = 2 \times 4 = 8

Answer:

25x^2 - 9y^2 = 8

Correct option: D. 8

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