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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

\[ =(4x-y)(x-4y) \]

 

 

 

 


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