Distributive Property and Combining Like Terms

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum or difference.

Front

How do you apply the Distributive Property to the expression 6(x - 3 + 5y)?

Back

You distribute 6 to each term inside the parentheses: 6 * x - 6 * 3 + 6 * 5y = 6x - 18 + 30y.

Front

What are like terms in an algebraic expression?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

Front

How do you combine like terms in the expression 7j + 3k + 10j - k?

Back

You combine the coefficients of like terms: (7j + 10j) + (3k - k) = 17j + 2k.

Front

What is the first step in simplifying the expression 5p + 7y + 2t - 3p + 4y?

Back

The first step is to identify and combine like terms: (5p - 3p) + (7y + 4y) + 2t.

Front

What is the result of combining like terms in the expression 5p + 7y + 2t - 3p + 4y?

Back

The result is 2p + 11y + 2t.

Front

How do you simplify the expression 3(9 + 2d) + 4d?

Back

First, apply the Distributive Property: 3 * 9 + 3 * 2d + 4d = 27 + 6d + 4d. Then combine like terms: 27 + 10d.

Front

What is the importance of the Distributive Property in algebra?

Back

The Distributive Property is important because it allows for the simplification of expressions and the solving of equations by distributing factors across sums or differences.

Front

Can you give an example of using the Distributive Property with negative numbers?

Back

Yes, for example, -2(x - 4) = -2x + 8, where -2 is distributed to both x and -4.

Front

What is the simplified form of the expression 2(c - 8)?

Back

The simplified form is 2c - 16, obtained by distributing 2 to both c and -8.