Find each product. (x−1)(x+2)

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.