Question

$x^2+5x+5y-y^2$

factorise by the formula

i.e $(a+b)(a-b)=a^2-b^2$​

Answer 1

Question :

⠀⠀⠀⠀⠀▪︎⠀Factorise : x² + 5x + 5y - y² .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀¤ Factorising x² + 5x + 5y - y² :

$\qquad \dashrightarrow \sf x^2 + 5x + 5y - y^2\:\\\\\qquad \dashrightarrow \sf x^2 - y^2 + 5x + 5y \:$

As, We know that ,

$\qquad \dag\:\:\bigg\lgroup \sf{ \:\:Algebraic \:Indentity\:\::\: a^2 - b^2 \:=\:(a + b ) ( a - b )}\bigg\rgroup \\\\\qquad \dashrightarrow \sf x^2 - y^2 + 5x + 5y \:\\\\\qquad \dashrightarrow \sf ( x + y ) ( x - y ) + 5x + 5y \:\\\\\qquad \dashrightarrow \sf ( x + y ) ( x - y ) + 5 ( x + y )\:\\\\\qquad \dashrightarrow \sf ( x + y ) ( x - y ) + 5 \:\\\\\qquad \dashrightarrow \sf ( x + y ) ( x - y + 5 ) \:\\\\ \dashrightarrow \underline {\boxed{\pmb{\frak{\purple { ( x + y ) ( x - y + 5 ) }}}}}\:\\\\\qquad \therefore \underline {\sf Hence, \:Factors \:of \: x^8 - x^4 - 30 \:are \:\pmb{\bf ( x + y ) ( x - y + 5 ) }\:.\:}$