Question

Factorise 4p² + 16pq + 16q² using appropriate identity, then its value is equal to
(2p + 4q)²
20p³q³
(2p + 4q) (2p - 4q)
(2p - 4q)²​

Answer 1

We have to factorise 4p² + 16pq + 16q² using appropriate identity, then its value is equal to ...

1. (2p + 4q)²
2. 20p³q³
3. (2p + 4q)(2p - 4q)
4. (2p - 4q)²

solution : 4p² + 16pq + 16q²

= (2p)² + 2 × (2p) × (4q) + (4q)²

if we assume 2p = a and 4q = b

we see, a² + 2ab + b² and it is equal to (a + b)² [ it is an algebraic identity ]

so, (2p)² + 2 × (2p) × (4q) + (4q)² = (2p + 4q)²

hence, the value of 4p² + 16pq + 16q² = (2p + 4q)² .i.e., option (1) is correct choice.

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