Question

Factor the expression. k2 + 5kf – 50f2

Answer 1

We have

k^2 - 25f^2 + 5kf - 25f^2 =

k^2 - (5f)^2 + 5f( k - 5f) =

( k - 5f )( k + 5f ) + 5f( k - 5f ) =

( k - 5f )( k + 5f + 5f ) =

( k - 5f )( k + 10f );

Explanation:

Answer 2

Answer: The required factored form of the given expression is
`(k-5f)(k+10f).`

Step-by-step explanation: We are given to factor the following quadratic expression :

`E=k^2+5kf-50f^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

To factor the given expression, we need two integers with sum 5 and product -50 and those two integers are 10 and -5.

The factorization of expression (i) is as follows :

`E\\\\=k^2+5kf-50f^2\\\\=k^2+10kf-5kf-50f^2\\\\=k(k+10f)-5f(k+10f)\\\\=(k-5f)(k+10f).`

Thus, the required factored form of the given expression is
`(k-5f)(k+10f).`