Multiplying Polynomials

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, $$2x^2 + 3x - 5$$ is a polynomial.

Multiplying polynomials involves using the distributive property to combine each term in one polynomial with each term in another polynomial.

The square of a binomial, such as $$(a + b)^2$$ , is calculated using the formula: $$a^2 + 2ab + b^2$$ .

The expanded form is $$x^2 + 9x + 18$$ .

The FOIL method is a technique for multiplying two binomials. It stands for First, Outside, Inside, Last, referring to the order in which you multiply the terms.

The result is $$2x^2 - 3x - 14$$ .

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

A coefficient is a numerical factor in a term of a polynomial. For example, in $$4x^2$$ , 4 is the coefficient.

The degree of a polynomial is the highest power of the variable in the expression. For example, the degree of $$3x^4 + 2x^2 + 1$$ is 4.

The result is $$2x^5 - 4x^4 - 6x^3$$ .