(viii) 2(x²-4)=3(x²-4)
Answers
Answer:
Step-by-step explanation:
Using the distributive property, you get:
3x^3 + 2x^2 - 12x - 8
So that’s what you get when you apply the FOIL method.
But… what if we set the original algebraic expression equal to something, like 0?
(x^2 - 4)(3x + 2) = 0
This would give us two possible solutions to this equation. Basically, you make the contents of one of the parentheses equal to 0, and then solve for x in the other one. Then repeat this for the other possible value of x.
Let’s work on the set of parentheses to the left, first. Remember that we need to choose a value for x such that the contents of that set of parentheses is equal to 0:
(x^2 - 4)
This means x^2 must equal positive 4; add them together and you get 0.
Because x is being squared, there are two possible solutions that will make the entire statement true:
x = 2
x = -2
Because BOTH, when squared, will yield positive 4:
(x^2 - 4) = 0
x = -2
(-2^2 - 4) = 0
(4 - 4) = 0
0 = 0
(x^2 - 4) = 0
x = 2
(2^2 - 4) = 0
4–4 = 0
0 = 0
So far we have two solutions for x: x}(2, -2)
So what about the other set of parentheses?
(3x+2) = 0
This means that 3x must equal -2 in order to make this statement true.
to solve for this, solve it as you would any other equation and solve for x.
3x + 2 = 0
Subtract 2 from both sides:
3x = -2
Divide both sides by 3:
x = -2/3
So, we have found all three values for x. The last thing to do is to plug them back into the equation, one at a time, to double-check that they all result in a true statement:
(x^2–4)(3x+2) = 0
x = -2
(-2^2 - 4)(3*-2+2) = 0
(4–4)(-6+2) = 0
0(-4) = 0
0 = 0
So that’s one down; x = -2.
(x^2–4)(3x+2) = 0
x = 2
(2^2–4)(3*2+2) = 0
(4–4)(6+2) = 0
0(8) = 0
0 = 0
That’s two down; x = -2 or 2.
(x^2–4)(3x+2) = 0
x = -2/3
((-2/3)^2–4)(3*(-2/3)+2) = 0
(4/9–4)((-6/3)+2) = 0
(-32/36)(-2+2) = 0
(-8/9)(0) = 0
0 = 0
So x can be one of three different values:
x = 2
x = -2
x = -2/3