Factoring, Simplifying Expressions (24/25 - Math 7)

Front

What is the process of combining like terms in an expression?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, in the expression 5a + 2b - 3a + 4, you combine 5a and -3a to get 2a, resulting in 2a + 2b + 4.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors. For example, the expression 8x - 10 can be factored as 2(4x - 5).

Front

How do you simplify the expression -9(7y - 2) + 12 - y?

Back

To simplify, distribute -9 to both terms inside the parentheses: -63y + 18. Then combine with the other terms: -63y + 18 + 12 - y = -64y + 30.

Front

What is the result of multiplying (x - 6) by 4?

Back

The result is 4x - 24, obtained by distributing 4 to both terms in the parentheses.

Front

How do you combine like terms in the expression 3x + 2x + 3y - 7y?

Back

Combine the x terms (3x + 2x = 5x) and the y terms (3y - 7y = -4y) to get 5x - 4y.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 2x and 5x are like terms, while 2x and 3y are not.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parentheses.

Front

How do you factor the expression 12x + 8?

Back

You can factor out the greatest common factor, which is 4, resulting in 4(3x + 2).

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that two or more numbers share. For example, the GCF of 12 and 8 is 4.

Front

What does it mean to simplify an expression?

Back

Simplifying an expression means to reduce it to its simplest form by combining like terms and eliminating unnecessary parentheses.