Simplifying the Expression (v^2-36)(6-v)

Simplifying algebraic expressions is a fundamental skill in high school mathematics. In this article, we will walk through the step-by-step process of simplifying the expression (v^2-36)(6-v).

Step 1: Understand the expression

The expression (v^2-36)(6-v) is a multiplication of two binomials. A binomial is an algebraic expression with two terms. In this case, the first binomial is v^2-36 and the second binomial is 6-v.

Step 2: Distribute the multiplication

To simplify the expression, we need to distribute the multiplication. This means we will multiply each term in the first binomial with each term in the second binomial.

The distribution can be represented as: (v^2-36)(6-v) = v^2(6-v) - 36(6-v)

Step 3: Multiply the first term

Multiplying the first term of the first binomial (v^2) with the first term of the second binomial (6) gives us: v^2(6) = 6v^2

Step 4: Multiply the first term with the second term

Multiplying the first term of the first binomial (v^2) with the second term of the second binomial (-v) gives us: v^2(-v) = -v^3

Step 5: Multiply the second term

Multiplying the second term of the first binomial (-36) with the first term of the second binomial (6) gives us: -36(6) = -216

Step 6: Multiply the second term with the second term

Multiplying the second term of the first binomial (-36) with the second term of the second binomial (-v) gives us: -36(-v) = 36v

Step 7: Combine the results

Combining the results from steps 3-6, we get: (v^2-36)(6-v) = 6v^2 - v^3 - 216 + 36v

Step 8: Simplify the expression

The final simplified expression is: (v^2-36)(6-v) = 6v^2 - v^3 - 216 + 36v

By following these steps, you can simplify any algebraic expression involving the multiplication of two binomials.