could someone help me with this math problem?

Question

Factor the following.

 

16r^2-24r+9

Answer 1

Remember F-O-I-L (First-Outside-Inside-Last). 

 

When an expression like (ax+b)(cx+d) is expanded using the Distributive Property (twice) it is:

    (ax+b)(cx+d)

    ax(cx+d)  +  b(cx+d)

     acx²  +  axd   +   bcx   +   bd

       F          O           I            L

      acx²   + (ad+bc)x   + bd

 

 

"To factor" means to find the values that were multiplied to get the expression.  What factors produced:

     16x²    -24x  +  9

We need to find the values of:  a,b,c,d

    ac = 16

    (ad+bc)= -24

    bc = 9

 

     For a perfect square:  (ax+b)(ax+b), this is  a²=16, 2ab=-24, b²=9.  So, a=4 and b=-3, right?  (4x-3)²

 

PLZ try to learn the various methods for finding numbers that add to produce a value and multiply to produce another value.  Also, learn to use the Quadratic Formula.

       16x² - 24x + 9 = 0

       Using the Quadratic Formula, the values of x that satisfy the equation are:   3/4 and 3/4   which means

                 (x - 3/4)(x - 3/4) = 0

                  (4x - 3)(4x - 3)            [multiply by 4 and by 4 to get rid of fractions]

 

So,  a=4, b=-3. c=4, d=-3

 

This is a perfect square (which is likely the topic you are currently studying.)

 

To check:  Apply F-O-I-L to  (4x - 3)(4x - 3):

      F        O        I        L

    16x²  - 12x  - 12x  + 9

    16x² -24x + 9             Check!