Solve 25^3-1=(25-1)(25^2+25+1)=24(25^2+26)

$$25 ^ { 3 } - 1 = ( 25 - 1 ) ( 25 ^ { 2 } + 25 + 1 ) = 24 ( 25 ^ { 2 } + 26 )$$

Verify

Solution Steps

Calculate 25 to the power of 3 and get 15625.

$$15625-1=\left(25-1\right)\left(25^{2}+25+1\right)\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Subtract 1 from 15625 to get 15624.

$$15624=\left(25-1\right)\left(25^{2}+25+1\right)\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Subtract 1 from 25 to get 24.

$$15624=24\left(25^{2}+25+1\right)\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Calculate 25 to the power of 2 and get 625.

$$15624=24\left(625+25+1\right)\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Add 625 and 25 to get 650.

$$15624=24\left(650+1\right)\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Add 650 and 1 to get 651.

$$15624=24\times 651\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Multiply 24 and 651 to get 15624.

$$15624=15624\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Compare 15624 and 15624.

$$\text{true}\text{ and }\left(25-1\right)\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Subtract 1 from 25 to get 24.

$$\text{true}\text{ and }24\left(25^{2}+25+1\right)=24\left(25^{2}+26\right)$$

Calculate 25 to the power of 2 and get 625.

$$\text{true}\text{ and }24\left(625+25+1\right)=24\left(25^{2}+26\right)$$

Add 625 and 25 to get 650.

$$\text{true}\text{ and }24\left(650+1\right)=24\left(25^{2}+26\right)$$

Add 650 and 1 to get 651.

$$\text{true}\text{ and }24\times 651=24\left(25^{2}+26\right)$$

Multiply 24 and 651 to get 15624.

$$\text{true}\text{ and }15624=24\left(25^{2}+26\right)$$

Calculate 25 to the power of 2 and get 625.

$$\text{true}\text{ and }15624=24\left(625+26\right)$$

Add 625 and 26 to get 651.

$$\text{true}\text{ and }15624=24\times 651$$

Multiply 24 and 651 to get 15624.

$$\text{true}\text{ and }15624=15624$$

Compare 15624 and 15624.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$