Question

factorise :x^2 +2ax + a^2 -b^2​

Answer 1

Answer:

$\large \bold\red{(x + a + b)(x + a - b)}$

Step-by-step explanation:

We have to factorise,

${x}^{2} + 2ax + {a}^{2} - {b}^{2}$

Simplifying further,

We get,

$= ({x}^{2} + 2ax + {a}^{2} ) - {b}^{2}$

But,

We know that,

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

Therefore,

We get,

$= {(x + a)}^{2} - {b}^{2}$

But,

We know that,

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

Therefore,

We get,

$= \large \bold{(x + a + b)(x + a - b)}$

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

We have to use factorise method to get answer

$\tt{{x}^{2} + 2ax + {a}^{2} - {b}^{2}}$

Simplifying further .We get,

$= ({x}^{2} + 2ax + {a}^{2} ) - {b}^{2}$

But, We know that,

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

Therefore, We get :-

$= {(x + a)}^{2} - {b}^{2}=(x+a)$

But, We know that :-

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

Therefore, We get :-

$= \large \sf{(x + a + b)(x + a - b)}$