Equivalent Expressions

An equivalent expression is an expression that has the same value as another expression for all values of the variables involved.

To simplify an expression means to combine like terms and reduce it to its simplest form.

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

To combine like terms, add or subtract their coefficients while keeping the variable part the same. For example, $$3x + 5x = 8x$$ .

The distributive property states that $$a(b + c) = ab + ac$$ . It allows you to multiply a term by a sum.

Factoring an expression involves rewriting it as a product of its factors. For example, $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ .

A polynomial is an expression that consists of variables raised to whole number powers and their coefficients, such as $$2x^2 + 3x - 5$$ .

The degree of a polynomial is the highest power of the variable in the expression. For example, the degree of $$2x^3 + 3x^2 - 5$$ is 3.

Expanding an expression involves using the distributive property to remove parentheses and combine like terms.

A quadratic expression is a polynomial of degree 2, typically in the form $$ax^2 + bx + c$$ .