Factorize a² − b² − 4a + 4

Correct Answer is : (a − 2 + b)(a - 2- b)

Correct Answer is : (a − 2 + b)(a - 2- b)

Test Index

JAMB Mathematics 2015 Paper

Question : 61

Total: 61

Factorize

a^2 − b^2 − 4a + 4

Solution:

Concept:

Use grouping to form a perfect square, then apply the difference of two squares.

Explanation:

Rewrite the expression by grouping the terms in

a

a^2 - b^2 - 4a + 4 = (a^2 - 4a + 4) - b^2

Notice that

a^2 - 4a + 4 = (a - 2)^2

So the expression becomes:

(a - 2)^2 - b^2

This is now a difference of two squares:

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

Here,

x = a - 2

and

y = b

Therefore:

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

Answer:

(a - 2 + b)(a - 2 - b)

This matches option B.

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