91Ó°ÊÓ

Multiplying algebraic expressions is often simpler than it appears. The main goal is to combine similar parts of the expression.

First, let’s look at the coefficients (the numbers before the variables). When you multiply them together, you just do basic multiplication.

So, in the exercise, we multiply 8 and 9 to get 72.

Second, focus on the variables and their exponents. For variables with the same base, you add the exponents together.

For instance, in the given expression, you perform: \[ x^5 \times x = x^{5+1} = x^6 \]

Combining these steps, you get: \[ 8 x^5 \times 9 x = 72 x^6 \]

Simply put, multiply the numbers and add the exponents of similar variables.

Dividing algebraic expressions involves a couple of straightforward operations. You divide the coefficients and handle the variables separately.

For coefficients, just perform basic division.

The coefficients 72 and 6 divide to give 12: \[ \frac{72}{6} = 12 \]

For the variables, remember the rule: when you divide powers with the same base, subtract their exponents.

In the exercise, you perform: \[ \frac{x^6}{x^3} = x^{6-3} = x^3 \]

Thus, the division of the expression results in: \[ \frac{72x^6}{6x^3} = 12x^3 \]

By dividing correct coefficients and adjusting exponents, you can simplify even complex-looking expressions.

Combining like terms is crucial for simplifying expressions as it groups similar terms together.

Like terms have the same variable raised to the same power. For example, in terms like \[ 3x^2, 7x^2, \] the variable and exponent are identical, so they can be combined.

Consider the expression: \[ 5x^3 + 2x^3 \]

You can combine these by adding the coefficients only: \[ (5+2)x^3 = 7x^3 \]

In the original exercise, after performing multiplication and division, what remains is already a single term: \[ 12x^3 \]

When dealing with more complex expressions, always look for like terms you can combine to make the expression as simple as possible.

This will save time and make calculations easier in all algebraic problems.