The area of the base of a prism can be expressed as x2 + 4x + 1 and the height of the prism can be expressed as x - 3. What is the volume of this prism in terms of x?
Because the formula for the volume of a prism is V = Bh, where B is the field of the base and h is the height of the prism, V = (x - 3)(x^{2} + 4x + 1). Use the distributive property to multiply the ?rst term of the binomial, x, through each term of the trinomial, and then the second term of the binomial, -3, through each term of the trinomial: x(x^{2} + 4x + 1) 3(x^{2}+ 4x + 1). Then distribute: (x • x2) + (x • 4x) + (x • 1) - (3 • x2) - (3 • 4x) - (3 • 1). Simplify by multiplying inside each term: x^{3} + 4x^{2} + x - 3x^{2} - 12x - 3. Use the commutative property to arrange such as terms further to each other. Notice which 1x = x: x3 + 4x^{2} - 3x^{2} + x -12x - 3; combine like terms: x^{3} + x^{2} - 11x - 3.