^ means exponents.. so if it's 6^2 the answer is 36.. for people who don't know what it is
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I'll attempt to answer your Q. by considering the general case - then, if you can understand that, you'll know what to do with every expression you meet that looks like that . . .
Your expression is of the form: (a + b).(c + d).
To expand that, we multiply every term in the first bracket by every term in the second one, because brackets mean 'multiply'.
So, we get: a x c + a x d + b x c + b x d
And that simplifies to a.c.+ a.d + b.c + b.d
Frequently, a simplification of that expression is possible - as it is in your example.
So, let's now look at your particular expression.
You have: (2x^2+4x)(3x^3-7).
So, we get: 2x^2.3x^3 + 2x^2.(-7) + 4x.3x^3 +4x.(-7)
And that is: 6x^5 - 14x^2 + 12x^4 - 28x, using the rule that x^p.x^q = x^(p + q).
It is customary to arrange an expression like that in descending powers of x,
so we get: 6x^5 + 12x^4 - 14x^2 - 28x
The co-efficients all have 2 as a common factor, so we can now write:
2(3x^5 + 6x^4 - 7x^2 - 14x).
The co-efficients all have x as a common factor, so we can now write:
2x(3x^4 + 6x^3 - 7x - 14)
The expression in the bracket is of the form ax^4 + bx^3 + cx^2 + dx + e.
In that expression, none of the co-efficients a, b, c, d and the constant term e have any common factors (note that in our expression, c = 0). Hence, the expression has been simplified as much as possible.
► So the final result is: 2x(3x^4 + 6x^3 - 7x - 14)
Your expression is of the form: (a + b).(c + d).
To expand that, we multiply every term in the first bracket by every term in the second one, because brackets mean 'multiply'.
So, we get: a x c + a x d + b x c + b x d
And that simplifies to a.c.+ a.d + b.c + b.d
Frequently, a simplification of that expression is possible - as it is in your example.
So, let's now look at your particular expression.
You have: (2x^2+4x)(3x^3-7).
So, we get: 2x^2.3x^3 + 2x^2.(-7) + 4x.3x^3 +4x.(-7)
And that is: 6x^5 - 14x^2 + 12x^4 - 28x, using the rule that x^p.x^q = x^(p + q).
It is customary to arrange an expression like that in descending powers of x,
so we get: 6x^5 + 12x^4 - 14x^2 - 28x
The co-efficients all have 2 as a common factor, so we can now write:
2(3x^5 + 6x^4 - 7x^2 - 14x).
The co-efficients all have x as a common factor, so we can now write:
2x(3x^4 + 6x^3 - 7x - 14)
The expression in the bracket is of the form ax^4 + bx^3 + cx^2 + dx + e.
In that expression, none of the co-efficients a, b, c, d and the constant term e have any common factors (note that in our expression, c = 0). Hence, the expression has been simplified as much as possible.
► So the final result is: 2x(3x^4 + 6x^3 - 7x - 14)