Question

A rectangle has a height of 2x^4 with a width of x^2+8x+15. Express the area of the rectangle.

Answer 1

Hi there!

We know that the formula for the area of a rectangle is height * width. Thus, we can multiply these two expressions together:

$2x^4\cdot (x^2+8x+15)$

Now, we know through the distributive property that we can distribute the $2x^4$ to everything in the parenthesis. Once this is done, we get:

$2x^4 \cdot x^2+2x^4\cdot8x+2x^4\cdot15$

Now, we know through the power rule that when two exponents are multiplied together with the same base, the exponent can be added together $(x^a \cdot x^b = x^{a+b})$. This then would make our equation:

$2x^{4+2}+16x^{4+1}+30x^4$

Giving us for our final answer:

$2x^{6}+16x^{5}+30x^4$

Hope this helps!