Question

A rectangle has a height of a² + 3 and a width of a² + 2a + 5.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.​

Answer 1

Answer:

Area =  $a^4+2a^3+8a^2+6a+15$

Step-by-step explanation:

The area of a rectangle is given by:

Area = Height * Width

The expressions for height and width are given. We just need to multiply and add like terms (if applicable) to find the expression for the area of the rectangle.

Remember to use distributive property:

$(a+b)(x+y) = ax + ay + bx + by$

Thus, we have:

$(a^2+3)(a^2+2a+5)\\=(a^2)(a^2)+(a^2)(2a)+(a^2)(5)+3a^2+6a+15\\=a^4+2a^3+5a^2+3a^2+6a+15\\=a^4+2a^3+8a^2+6a+15$

THis is the expression for area.