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BECE Mathematics 2023 Paper

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Question : 23

Total: 40

Simplify:

(x-1)^2-1

$x^2 - 2x$
$x^2 + 2x$
$x^2 - 2x - 1$
$x^2 - 2x + 1$

Solution:

Concept:

Use the algebraic identity

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

.

Explanation:

Write

(x-1)^2

as

(x-1)(x-1)

.

Expand:

(x-1)(x-1) = x^2 - x - x + 1

.

Combine like terms:

x^2 - 2x + 1

.

Now subtract

1

from the expansion:

(x-1)^2 - 1 = (x^2 - 2x + 1) - 1

.

Simplify:

x^2 - 2x + 1 - 1 = x^2 - 2x

.

Thus, the simplified form is

x^2 - 2x

.

Answer:

Option A:

x^2 - 2x

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