Expanding and Factoring Expressions

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you simplify the expression -2(6n + 3) using the distributive property?

Back

By applying the distributive property: -2 * 6n + (-2) * 3 = -12n - 6.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors.

Front

What is the factored form of 6x + 12?

Back

6(x + 2).

Front

How do you factor the expression 12x + 8y - 4z completely?

Back

Factor out the greatest common factor, which is 4: 4(3x + 2y - z).

Front

What is the greatest common factor (GCF)?

Back

The GCF is the largest factor that divides two or more numbers or terms.

Front

How do you factor the expression 16x + 24x²?

Back

Factor out the GCF, which is 8x: 8x(2 + 3x).

Front

What is the purpose of factoring in algebra?

Back

Factoring helps simplify expressions, solve equations, and find roots of polynomials.

Front

How do you factor the expression -10m - 35 using a negative factor?

Back

Factor out -5: -5(2m + 7).

Front

What is a polynomial?

Back

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.