Question

(x+y) (2x+3y)-(x+y) (x+1) factorise the following expressions

Answer 1

SOLUTION :

FACTORISATION :

$\longrightarrow{\sf (x+y)(2x+3y)-(x+y)(x+1)}$

• Taking x+y as common :

$\implies \sf{( x+ y)\bigg[(2x + 3y) - (x + 1) \bigg] }$

$\implies \sf{( x+ y)(2x + 3y - x - 1)}$

$\implies \sf{( x+ y) (2x - x + 3y- 1) }$

$\implies \underline{\boxed{\bf{( x+ y)(x + 3y - 1 )}}}$

Simplification :

$\longrightarrow{\sf (x+y)(2x+3y)-(x+y)(x+1)}$

$\longrightarrow\sf \bigg[ 2x (x+y)+3y (x+y)\bigg] -\bigg[x (x+y)+1(x+y) \bigg]$

$\longrightarrow\sf (2x^2+2xy+3xy+3y^2)-(x^2 + xy+x+y )$

$\longrightarrow\sf 2x^2+2xy+3xy+3y^2-x^2 -xy - x - y$

$\longrightarrow\sf 2x^2-x^2+3y^2 +2xy+3xy- xy- x - y$

$\longrightarrow\bf x^2 + 3y^2+4xy-x - y$