Question

Factorise: 9x^2+6x+1-25y^2

Answer 1

9x^2+6x+1-25y^2
(3x)^2+2*3x*1+(1)^2-(5y)^2
(3x+1)^2-(5y)^2
{(3x+1)+5y}{(3x+1)-5y}
(3x+5y+1)(3x-5y+1)

Answer 2

Answer:

The factorisation of the given expression $9 x ^ { 2 } + 6 x + 1 - 25 y ^ { 2 }$ gives the values of $(3x+5y+1)(3x-5y+1)$

To find:

Factorisation of the given expression $9 x ^ { 2 } + 6 x + 1 - 25 y ^ { 2 }$

Solution:

Given expression is,

$9 x ^ { 2 } + 6 x + 1 - 25 y ^ { 2 }$

Splitting out the terms, we get,

$\begin{aligned} = ( 3 x ) ^ { 2 } & + 2 ( 3 x ) ( 1 ) + ( 1 ) ^ { 2 } - ( 5 y ) ^ { 2 } \\\\ & = ( 3 x + 1 ) ^ { 2 } - ( 5 y ) ^ { 2 } \end{aligned}$

We know that the value of

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

By using this formula in the above expression,  

Thus, the given expression becomes,

$\begin{array} { c } { 9 x ^ { 2 } + 6 x + 1 - 25 y ^ { 2 } } \\\\ { = ( 3 x + 1 + 5 y ) ( 3 x + 1 - 5 y ) } \\\\ { = ( 3 x + 5 y + 1 ) ( 3 x - 5 y + 1 ) } \end{array}$

Therefore, the factorisation of the given expression $9 x ^ { 2 } + 6 x + 1 - 25 y ^ { 2 }$ gives the values of $(3x+5y+1)(3x-5y+1)$