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(a + b)^2 Expansion and Visualisation

Factorise by ...

Question

Factorise by using formula: $a^{4} - (a^{2} - 3 b^{2})^{2}$

A

b^{2} (2 a^{2} - 3 b^{2})

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B

3 b^{2} (a^{2} - 3 b^{2})

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C

3 b^{2} (2 a^{2} - 3 b^{2})

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D

3 b^{2} (2 a^{2} - b^{2})

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Solution

The correct option is B $3 b^{2} (2 a^{2} - 3 b^{2})$
$F a c t o r i z i n g {(a^{2})}^{2} - {a^{2} {- 3 b}^{2}}^{2}, = ({a^{2} - a}^{2} {+ 3 b}^{2}) (a^{2} {{+ a}^{2} - 3 b}^{2}) = (2 a^{2} - 3 b^{2}) (3 b^{2})$

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Similar questions

Q. Factorise by using formula:

(5 a - 3 b)^{2} - 16 b^{2}

a^{2} - (2 a + 3 b)^{2}

Q. Subtract the sum of

12 a b - 10 b^{2} - 18 a^{2}

9 a b + 12 b^{2} + 14 a^{2}

from the sum of

a b + 2 b^{2}

3 b^{2} - a^{2} .

2 a + 6 b - 3 (a + 3 b)^{2}

2 a + 6 b - 3 (a + 3 b)^{2}

= 2 (a + 3 b) - 3 (a + 3 b)^{2} [T a k i n g 2 c o m m o n f r o m 2 a + 6 b]

= (a + 3 b) {\begin{matrix} 2 - 3 (a + 3 b) \end{matrix}} [T a k i n g (a + 3 b) c o m m o n]

= (a + 3 b) (2 - 3 a - 9 b)

Factories :

$(i) (a - 3 b)^{2} - 36 b^{2} (i i) 25 (a - 5 b)^{2} - 4 (a - 3 b)^{2} (i i i) a^{2} - 0.36 b^{2} (i v) a^{4} - 625 (v) x^{4} - 5 x^{2} - 36 (v i) 15 (2 x - y)^{2} - 16 (2 x - y) - 15$

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