Question

factorize 3y2-24y+48

Answer 1

Answer:

3(y - 4)²

Explanation

Factorise:

Factorise:3y² - 24y + 48

Taking the highest common factor out Here, 3 is the common factor of the terms.

⟹ 3 ( y² - 8y + 16 )

Splitting the middle term ( -8 ) such that the numbers sum up to 8 and their product is 16.

⟹ 3 ( y² - 4y - 4y + 16 )

Taking out common Factor from the first two terms inside the brackets.

⟹ 3 [ y( y - 4 ) - 4y + 16 ]

Taking out the common Factor from the remaining terms inside the brackets.

⟹ 3[ y( y - 4 ) -4 ( y - 4 ) ]

Taking out ( y - 4 ) as common from the terms inside the brackets

⟹ 3 ( y - 4 )( y - 4 )

or

⟹ 3( y - 4 )²

Alternate Solution:

3y² - 24y + 48

( Taking common factor out )

⟹ 3 ( y² - 8y + 16 )

⟹ 3 [ (y)² - 2(y)(4) + (4)² ]

By using identity: a² + 2ab + b² = (a + b)². Here, y corresponds with a and 4 corresponds with b.

⟹ 3 ( y + 4 )²