Hi there!
We know that the formula for the area of a rectangle is height * width. Thus, we can multiply these two expressions together:
[tex]2x^4\cdot (x^2+8x+15)\\[/tex]
Now, we know through the distributive property that we can distribute the [tex]2x^4\\[/tex] to everything in the parenthesis. Once this is done, we get:
[tex]2x^4 \cdot x^2+2x^4\cdot8x+2x^4\cdot15[/tex]
Now, we know through the power rule that when two exponents are multiplied together with the same base, the exponent can be added together [tex](x^a \cdot x^b = x^{a+b})[/tex]. This then would make our equation:
[tex]2x^{4+2}+16x^{4+1}+30x^4\\[/tex]
Giving us for our final answer:
[tex]2x^{6}+16x^{5}+30x^4\\[/tex]
Hope this helps!
