Question

Factorise (25a2+C2+10ac)-49b2

Answer 1

Answer:

$\large \bold\red{ (5a + 7b + c)(5a - 7b + c)}$

Explanation:

Given,

$(25 {a}^{2} + {c}^{2} + 10ac) - 49 {b}^{2}$

Further simplifying,

We get,

$= ( {(5a)}^{2} + {(c)}^{2} + 2(5a)(c)) - 49 {b}^{2}$

But,

We know that,

• $( {x}^{2} + {y}^{2} + 2xy ) = {(x + y)}^{2}$

Therefore,

We get,

$= {(5a + c)}^{2} - 49 {b}^{2} \\ \\ = {(5a + c)}^{2} - {(7b)}^{2}$

But,

We know that,

• ${x}^{2} - {y}^{2} = (x + y)(x - y)$

Tgerefore,

We get,

$= (5a + c + 7b)(5a + c - 7b) \\ \\ = \large \bold{ (5a + 7b + c)(5a - 7b + c)}$

Answer 2

Answer:

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