Question

express y^2 - 9y + 20 as product of two expressions​

Answer 1

Question : Express y² - 9y + 20 as a product of two expressions.

Solution :

{Note : expressing something as a product of two expressions is nothing but finding the factors. So this problem's solution is nothing but finding the factors of y² - 9y + 20 , that is, factorization of the problem }

y² - 9y + 20

= y² - ( 5 + 4)y + 20

{ Since, -(5+4)= -9 and -5y × -4y = 20y² }

= y² - 5y - 4y + 20 { Solving the bracket }

= y ( y - 5) - 4 ( y - 5 )

{ Taking out the common factors }

= ( y - 5 ) ( y - 4 ) { factoring }

Therefore, y² - 9y + 20 as a product of two expressions is = ( y - 5 ) × ( y - 4 )

(Answer)

Answer 2

y² - 9y + 20 = (y - 4)(y - 5)

Given :

The expression y² - 9y + 20

To find

To express the expression as product of two expressions

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is y² - 9y + 20

Step 2 of 2 :

Express as product of two expressions

$\displaystyle \sf{ {y}^{2} - 9y + 20 }$

$\displaystyle \sf{ = {y}^{2} - (4 + 5)y + 20 }$

$\displaystyle \sf{ = {y}^{2} - 4y - 5y + 20 }$

$\displaystyle \sf{ = y(y - 4) - 5(y - 4)}$

$\displaystyle \sf{ = (y - 4) (y - 5)}$

Hence expressing y² - 9y + 20 as product of two expressions we get

y² - 9y + 20 = (y - 4)(y - 5)