Question

Simplify this expression.

2x3(5x3 - 7)

Answer 1

is that \[2x ^{3}\]

Answer 2

yes

Answer 3

2x^3(5x^3−7)=
2∗5x^3+3−2∗7x^3=
10x^6−14x^3

Answer 4

Oh yeah, in that 2∗5x^3+3−2∗7x^3 part, I should've made it 2∗5x^(3+3)−2∗7x^3

Answer 5

2x3(5x3-7)

Final result :

2x3 • (5x3 - 7)
Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3" was replaced by "x^3". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Raise x to the 3rd power
Exponentiation :

Equation at the end of step 1 :

(2 • (x3)) • ((5 • x3) - 7)
Step 2 :

Raise x to the 3rd power
Exponentiation :

Equation at the end of step 2 :

(2 • x3) • (5x3 - 7)
Step 3 :

Multiply 2x3 by 5x3-7
Trying to factor as a Difference of Cubes:

3.1 Factoring: 5x3-7

Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3

Check : 5 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes


Polynomial Roots Calculator :

3.2 Find roots (zeroes) of : F(x) = 5x3-7
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 5 and the Trailing Constant is -7.

The factor(s) are:

of the Leading Coefficient : 1,5
of the Trailing Constant : 1 ,7

Let us test ....

P Q P/Q F(P/Q) Divisor
-1 1 -1.00 -12.00
-1 5 -0.20 -7.04
-7 1 -7.00 -1722.00
-7 5 -1.40 -20.72
1 1 1.00 -2.00
1 5 0.20 -6.96
7 1 7.00 1708.00
7 5 1.40 6.72

Polynomial Roots Calculator found no rational roots

Trying to factor as a Difference of Cubes:

3.3 Factoring: 5x3-7

Check : 5 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes


Final result :

2x3 • (5x3 - 7)