Solve 2x^{2}*x^3-3x^4+25x^2*x^3=

$$2 x ^ { 2 } \cdot x ^ { 3 } - 3 x ^ { 4 } + 25 x ^ { 2 } \cdot x ^ { 3 } =$$

Evaluate

$$3\left(9x-1\right)x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2x^{5}-3x^{4}+25x^{2}x^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2x^{5}-3x^{4}+25x^{5}$$

Combine 2x^{5} and 25x^{5} to get 27x^{5}.

$$27x^{5}-3x^{4}$$

Factor

$$3\left(9x-1\right)x^{4}$$

Solution Steps

Factor out x^{2}.

$$x^{2}\left(2x^{3}-3x^{2}+25x^{3}\right)$$

Consider 2x^{3}-3x^{2}+25x^{3}. Factor out x^{2}.

$$x^{2}\left(2x-3+25x\right)$$

Consider 2x-3+25x. Multiply and combine like terms.

$$27x-3$$

Consider 27x-3. Factor out 3.

$$3\left(9x-1\right)$$

Rewrite the complete factored expression. Polynomial x^{2} is not factored since it does not have any rational roots.

$$3x^{2}x^{2}\left(9x-1\right)$$