PLEEASE PEALSE PLEASE HELP, 40 POINTS

FInd the roots of the equation 6a^2-3. If 6a=0

3 (a+1) (a-1)

STEP

1

:

Equation at the end of step 1

 3a2 -  3

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  3a2 - 3  =   3 • (a2 - 1)

Trying to factor as a Difference of Squares:

3.2      Factoring:  a2 - 1

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check :  a2  is the square of  a1

Factorization is :       (a + 1)  •  (a - 1)

Final result :

 3 • (a + 1) • (a - 1)

Step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3