Question

State whether the statement is True or False.

Evaluate: $(m+3)(m-3)(m^2+9)$ is equal to $m^4-81$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, $(m+3)(m-3)(m^2+9)$.

We know, $(a+b)(a-b)$ $=(a^2-b^2)$.

Multiply by using direct method, we get,

$(m+3)(m-3)(m^2+9)$$=[m^2-(3{)}^2\left]\right(m^2+9)$
$=(m^2-9)(m^2+9)$ $=(m^2+9)(m^2-9)$.

Now, by using formula $(a^2-b^2)=(a+b)(a-b)$, we get,

$=\left(\right(m^2{)}^2-\left(9{)}^2\right)$
$=m^4-81$.

Hence, the statement is true.

Therefore, option $A$ is correct.