Question

Evaluate the expression when $a = 9 \text{and} b = - 4$.

$b (25 a^2)$

Short answer

The value of the expression is$b (25 a^2) = -8100$.

Step-by-step solution

Step-1 – Apply the concept of product

When two or more numbers are multiplied together, it gives a number. The numbers that are being multiplied are called the factors. And the result of the multiplication of numbers is called the product of those numbers.

Step-2 – Associative Property of Multiplication of Real Numbers: 

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property: $\text{(a} · \text{b)} · \text{c}=\text{a} · ( \text{b} · \text{c} )$

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example: $\text{(6} · \text{4)} · \text{3}=\text{6} · ( \text{4} · \text{3} ) = 72$

Step-3 – Evaluate the expression

To evaluate the expression$b (25 a^2)$, substitute the value of a as 9 and the value of b as – 4 and multiply the numbers as shown below,

localid="1649084732545" $\begin{array}{l}b\left(25a^2\right)\\ -4(25·9^2)(\text{Substitute}a=9\text{and}b=-4)\\ =(-4·25)·81(\text{AssociativePropertyofMultiplication)}\\ =-100·81=-8100\end{array}$

Thus, the value of the expression is$b (25 a^2) = -8100$.