Find each product. (x−1)(x+2)

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Identify the problem as multiplying two binomials: $(x - 1)(x + 2)$.

Apply the distributive property (also known as FOIL method) to multiply each term in the first binomial by each term in the second binomial.

Multiply the first terms: $x \times x = x^{2}$.

Multiply the outer terms: $x \times 2 = 2x$.

Multiply the inner terms: $-1 \times x = -x$, and multiply the last terms: $-1 \times 2 = -2$. Then combine all these results into one expression: $x^{2} + 2x - x - 2$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Multiplication

Polynomial multiplication involves multiplying each term in one polynomial by each term in the other. This process combines like terms to simplify the expression. For binomials, this often uses the distributive property or FOIL method.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a parenthesis, which is essential when expanding products of polynomials.

Combining Like Terms

After multiplying polynomials, terms with the same variable and exponent are combined to simplify the expression. This step ensures the polynomial is written in its simplest form.

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