d Factorize 4 x 2 − 17 x y + 4y 2 factorization of given

# Question 5: Factorize 4 x 2 − 17 x y + 4y 2

Question 5: Factorize 4 x 2 − 17 x y + 4y 2

Factorization exercises , factorization examples

Solution:

To see as how to evaluate an expression for factorization, we write it;

$4x^2-17x+4y^2$

Multiply last term i-e ​$$4y^2$$​ with the first term ​$$4x^2$$​ we get  ​$$16x^2y^2$$​. So, we split mid term -17xy into two parts so that if we add these two parts we get -17xy —— and if these two parts are multiplied we get  ​$$16x^2y^2$$​.

We can think of (-16 xy) and (-1xy)because;

1- when added (-16xy) +(-1xy) = -16xy-xy= -17xy

2- when multiplied (-16xy) (-1xy) =  ​$$16x^2y^2$$

So, we write;

$=4x^2-16xy-1xy+4y^2$

Take 4x as common from first two terms and (-1y) as common from last two terms;

$= 4x(x-4y)-1y(x-4y)$

$=(4x-1y)(x-4y)$

or

$=(4x-y)(x-4y)$