Question

Find each product.

$\left(\mathbf{2}a-\mathbf{5}\right)\left(\mathbf{3}a+\mathbf{5}\right)$

Short answer

The product of$\left(2a-5\right)\left(3a+5\right)$ is $\mathbf{6}{a}^2-\mathbf{5}a-\mathbf{25}$.

Step-by-step solution

Step 1. Write distributive property.

For any numbers,$a,b$ and c, $a\left(b+c\right)=ab+ac$.

Step 2. Apply distributive property.

Apply distributive property to the given expression.

$2a\left(3a+5\right)-5\left(3a+5\right)=2a\cdot 3a+2a\cdot 5-5\cdot 3a-5\cdot 5$

Step 3. Multiply and simplify.

Multiply terms in the above expression and simplify it further.

$6a^2+10a-15a-25=6a^2-5a-25$

Therefore, the product of$\left(2a-5\right)\left(3a+5\right)$ is $6a^2-5a-25$.