An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. For example, 3x + 5 is an algebraic expression.

Terms are the individual parts of an algebraic expression, separated by plus or minus signs. In 3x + 5, both 3x and 5 are terms.

The coefficient is the numerical factor of a term in an algebraic expression. For example, in 3x, 3 is the coefficient.

A monomial is an algebraic expression that consists of only one term, such as 7xy.

To add algebraic expressions, combine like terms, which are terms with the same variables raised to the same power. For example, 3x + 4x = 7x.

A binomial is an algebraic expression that consists of two terms, such as a + b.

A polynomial is an algebraic expression with more than one term. For example, x² + 3x + 4 is a polynomial.

To multiply a monomial by another monomial, multiply the coefficients and then the variables. For example, 3x × 4x = 12x².

An identity in algebra is an equation that holds true for all values of its variables. For example, (a + b)² = a² + 2ab + b² is an identity.

Combining like terms means adding or subtracting terms that have the same variable and exponent. For instance, 2x and 3x are like terms and can be combined to make 5x.

To multiply a polynomial by a monomial, distribute the monomial to each term in the polynomial. For example, 3x × (x + 4) = 3x² + 12x.

A term is a part of an algebraic expression, separated by plus or minus signs, while a factor is a quantity that is multiplied by another quantity. In 3x, 3x is a term and 3 and x are factors.

To apply the identity (a + b)² = a² + 2ab + b², substitute the values of a and b into the formula. For example, if a = 2 and b = 3, (2 + 3)² = 4 + 12 + 9 = 25.

The product of (a + b)(a − b) is given by the identity a² − b².

To multiply polynomials, multiply each term in the first polynomial by each term in the second polynomial and combine like terms. For example, (x + 2) × (x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.

Algebraic expressions are used in finance for budgeting, construction for area calculations, and many other real-life scenarios where relationships between quantities need to be expressed mathematically.

To simplify an expression using a² − b² = (a + b)(a − b), identify the expression in the form of a² − b² and apply the identity. For example, x² − 4 = (x + 2)(x − 2).

A polynomial consists of terms that may include coefficients, variables, and exponents. The degree of the polynomial is determined by the highest exponent.

You can expand (x + y)² using the identity (a + b)² = a² + 2ab + b². For example, (x + y)² = x² + 2xy + y².

To subtract algebraic expressions, distribute the negative sign to each term of the expression being subtracted and then combine like terms.

Algebraic identities are crucial for simplifying complex expressions and solving equations more efficiently by applying known formulas.

To find the value of an algebraic expression for a given value of the variable, substitute the variable with the given value and perform the arithmetic operations.

In budgeting, if x represents the amount spent on groceries and y represents the amount spent on utilities, the total monthly expense can be expressed as x + y.

Like terms are terms in an algebraic expression that have the same variables raised to the same powers. They can be combined through addition or subtraction.

The distributive property states that a(b + c) = ab + ac. To simplify an expression, distribute the multiplier across the terms inside the parentheses.