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 multiply each term in one polynomial by each term in another polynomial.

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

To multiply a monomial by a polynomial, multiply the monomial by each term in the polynomial. For example, $$3x(2x^2 + 4x - 5) = 6x^3 + 12x^2 - 15x$$ .

The result is $$3x^3 - 12x^2 - 15x$$ .

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 $$x^2 - 4x - 21$$ .

The area of a rectangle is calculated using the formula $$A = l \cdot w$$ , where $$l$$ is the length and $$w$$ is the width.

The area is $$(x + 5)(x - 4) = x^2 + x - 20$$ .

The result is $$5x^3 - 13x^2 + 24x + 12$$ .