Question

X square +2xy+y square-1 factorise

Answer 1

$\textbf{ \huge{ \underline{ Hello Mate! }}}$

${x}^{2} + 2xy + {y}^{2} - 1$

In such cases, 1st notice do any formula is formed? Yes

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ = {(x + y)}^{2} - 1$

1 is very useful number factorisation since its square is also one only.

$= {(x + y)}^{2} - {1}^{2}$

Do this equation match any popular identity, yes!

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

$= (x + y + 1)(x + y - 1)$

Hence, factors are in multiplication so we get two factors out.

$\textsf{\red{ Factors are ( x + y + 1 )( x + y - 1 ) }}$

$\textbf{ Have great future ahead! }$

Answer 2

Answer:

+2xy+y

2

−1

In such cases, 1st notice do any formula is formed? Yes

\begin{gathered}{(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ = {(x + y)}^{2} - 1\end{gathered}

(a+b)

2

=a

2

+b

2

+2ab

=(x+y)

2

−1

1 is very useful number factorisation since its square is also one only.

= {(x + y)}^{2} - {1}^{2}=(x+y)

2

−1

2

Do this equation match any popular identity, yes!

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

2

−b

2

=(a+b)(a−b)

= (x + y + 1)(x + y - 1)=(x+y+1)(x+y−1)

Hence, factors are in multiplication so we get two factors out.

\textsf{\red{ Factors are ( x + y + 1 )( x + y - 1 ) }} Factors are ( x + y + 1 )( x + y - 1 )