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(a-b)^2 Expansion and Visualisation

Factorise a...

Question

Factorise $a - b - a^{2} + b^{2}$ :

A

(a - b) [1 - (a + b)]

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B

(a + b) [1 - (a - b)]

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C

(a - b) [1 - (a - b)]

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D

(a + b) [1 + (a - b)]

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Solution

The correct option is C $(a - b) [1 - (a + b)]$
$(a - b) - (a^{2} - b^{2})$
$= (a - b) - (a + b) (a - b)$
$= (a - b) [1 - (a + b)]$

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Similar questions

Factorize:

$a^{2} - b^{2} - 2 b - 1$

Q. Which step in the following problem is wrong?

a = b = 1

a = b

a^{2} = a b

a^{2} - b^{2} = a b - b^{2}

(a + b) (a - b) = b (a - b)

step-4: a + b =

\frac{b (a - b)}{a - b}

a + b = b

1 + 1 = 1

2 = 1

A = [\begin{matrix} 1 & - 1 2 & - 1 \end{matrix}], B = [\begin{matrix} a & 1 b & - 1 \end{matrix}]

(A + B)^{2} = A^{2} + B^{2}

a

b

[\begin{matrix} 1 & - 1 2 & - 1 \end{matrix}], B = [\begin{matrix} a & 1 b & - 1 \end{matrix}]

(A + B)^{2} = A^{2} + B^{2}

a

b

A = [\begin{matrix} 1 & - 1 \\ 2 & - 1 \end{matrix}], B = [\begin{matrix} a & 1 \\ b & - 1 \end{matrix}]

and (A + B)² = A² + B², values of a and b are
(a) a = 4, b = 1
(b) a = 1, b = 4
(c) a = 0, b = 4
(d) a = 2, b = 4

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