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# (4a-3)(4a+3)

Expand the following (4a-3) (4a+3) =

To do this problem, always think of use distributive law twice.

( 4a  -3 ) ( 4a+3) = (4 a +3 ) 4a - 3 (4a +3) =

16a2 + 12a - 12a - 9 = 16a-9

This way of thinking of use of distributive law will be very useful .

(X + a ) ( X+b ) = X( X +a ) +  b (  X + a) = X2 + aX + bX +ab = X2 +( a +b) X + ab

(X +a) ( X+b) = X2 + ( a + b) X + ab

To solve quadratic equation:

X2 + ( a+ b ) X + ab = 0        always factored  (X+a) ( X+b) =0

To evaluate the roots   ( X + a ) ( X +b ) =0      X+a =0  X1 = -a   X +b = 0   X2 = -b

X2 + ( a +b ) X + ab = X2 + ( X1 +X2 ) X + X1X2

Any Quadratic equation of aX2 + bX + c   =a (X2 +b/a X + c/a)

Sum of the roots is always : X1 + X2 = -b/a      X1 . X2 = c/a
So equation

3 X2 + 8X + 5 = ( 3X +5 ) ( X + 1)

( 3X + 5 ) 0   , then   X1 = -5/3     X2 = -1    Where X1 + X2 = -5/3 - 1 = -8/3

X1 . X2 = (-5/3) ( -1 ) = 5/3
See that gives us information about solving quadratic equations with factoring.

( X -a ) (X + a) =X2 - a2     ( where a+b equals a - a =0)

( X +a )2   = ( X + a) ( X + a) = X2 + 2a + a2       where a= b , and a +a = 2a

Always  methods which are obtained by use of the Principle( Distributive law), and information
will be used further must be emphasized.
When you expand binomials:
First you take the first part of the first expression (4a) times the first part of the second expression, which also happens to be (4a). Your answer to this part of the problem is 16a2.

Next, you deal with the middle term. In this case the middle term of the expanded equation is determined by the (-3) in the first binomial and the (4a) in the second binomial. Multiply them together to get the first number that will be combined, and that number is -12a. Now combine the 4a from the first binomial with the (+3) in the second binomial to get the second term that will be combined, and that number is 12a. Since -12a +12a equals zero, there is no middle term for this answer. Writing a "0" as a space holder is unnecessary. (When combining terms in the expression to get the middle term for the answer, multiply the two outside terms together, multiply the two inside terms together, and add those two answers together to get the middle term of the expansion.)

To get the third term for this expansion, multiply (-3) x (+3) to get -9.

So the answer for this expansion is 16a2-9.
For this you need to FOIL:
Multiply the first terms (4a)(4a) = 16a^2
Multiply the outer terms (4a)(3) = 12a
Multiply the inner terms (-3)(4a) = -12a
Multiply the last terms (-3)(3) = -9
Now you have:
16a^2 + 12a - 12a - 9
Combine like terms (12a - 12a cancel out) to get:
16a^2 - 9

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