Question

Find the product.

$\left(2x+5\right)\left(5x+2\right)$

Short answer

The final answer is $\mathbf{10}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{29}\mathit{x}\mathbf{+}\mathbf{10}$.

Step-by-step solution

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where,$a$ is any non-zero real number.

Step 3. Calculate the product (2x+5)(5x+2).

Use the power of a product rule to find the product.

$\begin{array}{c}\left(2x+5\right)\left(5x+2\right)=2x\left(5x+2\right)+5\left(5x+2\right)\\ =2x\left(5x\right)+2x\left(2\right)+5\left(5x\right)+5\left(2\right)\\ =10x^2+4x+25x+10\\ =10x^2+29x+10\end{array}$

Therefore, the final answer is $10x^2+29x+10$.