Question 91731
Factorise:
{{{a^2+6ab+9b^2-1}}} Rewrite this as:
{{{(a^2+6ab+9b^2)-1}}} Factorise the parentheses.
{{{(a+3b)(a+3b)-1}}} which can be written as:
{{{(a+3b)^2-1}}} Now you have a difference of two squares which can be factored...oops - factorised thus:
{{{A^2-B^2 = (A+B)(A-B)}}} Applying this to your problem,we get:
{{{(a+3b+1)(a+3b-1)}}}

Check the answer by multiplying the two factors.
{{{(a+3b+1)(a+3b-1) = a^2+3ab*cross(-a)+3ab+9b^2*cross(-3b)+cross(a)+cross(3b)-1}}} Simplify this.
{{{a^2+3ab+3ab+9b^2-1}}} Combine like-terms.
{{{a^2+6ab+9b^2-1}}} ...your original expression.