Question 146199
{{{(x+1)^2-y^2}}} Start with the given expression


Let {{{a=x+1}}}



{{{a^2-y^2}}} Replace {{{x+1}}} with "a"




{{{(a+y)(a-y)}}} Now factor the expression by use of the difference of squares formula. Remember, the difference of squares formula is {{{A^2-B^2=(A+B)(A-B)}}}



{{{(x+1+y)(x+1-y)}}} Replace each "a" with {{{x+1}}}



{{{(x+y+1)(x-y+1)}}} Rearrange the terms




So {{{(x+1)^2-y^2}}} factors to {{{(x+y+1)(x-y+1)}}}



In other words, {{{(x+1)^2-y^2=(x+y+1)(x-y+1)}}}