what is 49x^2-25 factored

Question

I need to know how to factor this polynomial 

Answer 1

The expression has the difference of two perfect squares.

49x^2 =(7x)² and 25 = 5²

The factors are then the sum and difference of the roots.

So (7x +5)(7x - 5) = 49x² -25

Answer 2

49x^2-25 =  (7x)^2-5^2                 (   49=7^2, 25=5^2        )

               = (7x+5)(7x-5)                (   a^2-b^2=(a+b)(a-b)   )

 

 

 

 

For a^2-b^2=(a+b)(a-b), the reason is like this:

 

(a+b)(a-b)= a*a + a*(-b) +  b*a  + b*(-b)

               = a^2     -ab      +  ab      -b^2

               =a^2 - b^2

 

Answer 3

Meredith, remember that x² - y² = (x-y)(x+y).  Does this help?

Answer 4

To factor X²-Y², you get (X+Y)(X-Y).

 

49x² and 25 are both squares, so your factors would be (7x+5)(7x-5)

 

I hope this helped, Meredith!