Question

factorise ( x+y)2+9(x +y)+20​

Answer 1

Answer:

$2x + 2y + 9x + 9y + 20 \\ 11x + 11y + 20 \\ 11(x + y) + 20$plz mark as brainlist

Answer 2

(x + y)² + 9(x + y) + 20 = ( x + y + 5 ) ( x + y + 4 )

Given :

The expression (x + y)² + 9(x + y) + 20

To find :

Factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is (x + y)² + 9(x + y) + 20

Step 2 of 2 :

Factorise the expression

$\sf {(x + y)}^{2} + 9(x + y) + 20$

Let a = x + y

Then the given expression

$\sf {(x + y)}^{2} + 9(x + y) + 20$

$\sf = {a}^{2} + (5 + 4)a + 20$

$\sf = {a}^{2} + 5a + 4a + 20$

$\sf = a(a + 5) + 4(a + 5)$

$\sf = (a + 5) (a+ 4)$

= ( x + y + 5 ) ( x + y + 4 ) [ Putting the value of a ]

(x + y)² + 9(x + y) + 20 = ( x + y + 5 ) ( x + y + 4 )

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