d Factorize 10 x 2 − 41 x y + 21y 2 factorization applicable

Question 2: Factorize 10 x 2 − 41 x y + 21y 2


Question 2: Factorize \( 10x^2-41xy+21y^2 \)

Factorization exercises , factorization examples

Solution :

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

\[ 10x^2-41xy+21y^2 \]

If we multiply last term i-e  ​\( 21y^2 \)​  with first term i-e ​\( 10x^2 \)​​ we get ​​\( \[ 210 x^2y^2 \] ​ \)

So we break mid term i-e ​\( -41xy \)​ into two parts -35xy and -6xy  such that;

1- If we add  these two parts we get  -41xy i-e (-35xy) + ( -6xy) = -41xy

2- If we multiply these two parts we get ​\( 210x^2y^2 \)​​ i-e (-35xy) (-6xy) = ​\( 210x^2y^2 \)


So, we can write;

\[ =10x^2 – 35xy-6xy+21y^2 \]

Taking common 5x from first two terms and -3y from last two terms; we get;

\[ =5x(2x-7y)-3y(2x-7y) \]


\[ =[5x(2x-7y)-3y(2x-7y)] \]

Now (2x-7y) can be taken as common;

\[ =(2x-7y)[5x-3y] \]


\[ =(2x-7y)(5x-3y) \]



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