Distribute, Combine Like Terms, Factor out

Front

What does it mean to distribute in algebra?

Back

To distribute means to multiply a term by each term inside a set of parentheses. For example, in the expression 2(4 + 9w), you would multiply 2 by both 4 and 9w, resulting in 8 + 18w.

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How do you combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For example, in the expression -10x + 15 - 3x + 2, you combine -10x and -3x to get -13x, and combine 15 and 2 to get 17.

Front

What is the process of factoring an expression?

Back

Factoring an expression involves rewriting it as a product of its factors. For example, the expression 4x - 16 can be factored as 4(x - 4).

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What is a common factor?

Back

A common factor is a number or expression that divides two or more numbers or expressions without leaving a remainder. For example, in the expression 4x - 16, the common factor is 4.

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What does it mean to factor completely?

Back

Factoring completely means breaking down an expression into its simplest factors, such that no further factoring is possible. For example, 4(x - 4) is the complete factorization of 4x - 16.

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 set of parentheses.

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How do you simplify an expression?

Back

To simplify an expression, you combine like terms and perform any operations to reduce it to its simplest form. For example, simplifying -10x + 15 - 3x + 2 results in -13x + 17.

Front

What is the significance of parentheses in algebraic expressions?

Back

Parentheses indicate which operations should be performed first in an expression. They help clarify the order of operations.

Front

What is the result of distributing -4 in the expression -4(-4d - 5)?

Back

Distributing -4 results in 16d + 20, as -4 is multiplied by both -4d and -5.

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What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents. Examples include 3x^2 + 2x - 5.