Polynomial Operations Warmup

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

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in the other polynomial, then combining like terms.

The distributive property states that $$a(b + c) = ab + ac$$ . It is used to multiply a single term by a sum or difference.

To multiply two binomials, use the FOIL method: First, Outer, Inner, Last. For example, for $$(a + b)(c + d)$$ , it becomes $$ac + ad + bc + bd$$ .

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

The square of a binomial $$(a + b)^2$$ is equal to $$a^2 + 2ab + b^2$$ .

The simplified expression is $$-4x^2 - 6x$$ .

To add polynomials, combine like terms by adding the coefficients of terms with the same degree.

Like terms are terms that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms.

The result is $$3x^3 + x^2 + x - 11$$ .