Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6) - 4(3y² - 4y +2)

검증된 단계별 안내

Distribute the 2 across each term inside the first parentheses: multiply 2 by each term in \(12y^{2} - 8y + 6\), resulting in \(2 \times 12y^{2}\), \(2 \times (-8y)\), and \(2 \times 6\).

Distribute the -4 across each term inside the second parentheses: multiply -4 by each term in \(3y^{2} - 4y + 2\), resulting in \(-4 \times 3y^{2}\), \(-4 \times (-4y)\), and \(-4 \times 2\).

Write out the expanded expression after distribution, combining all the terms obtained from both distributions.

Group like terms together: combine the \(y^{2}\) terms, the \(y\) terms, and the constant terms separately.

Simplify each group by adding or subtracting the coefficients of like terms to get the final simplified expression.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, a(b + c) = ab + ac. This is essential for expanding expressions like 2(12y² - 8y + 6) by multiplying 2 with each term inside the parentheses.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. For instance, 12y² and 3y² are like terms and can be combined by adding or subtracting their coefficients. This simplifies the expression after distribution.

Polynomial Subtraction

Polynomial subtraction requires careful handling of the minus sign before parentheses. When subtracting polynomials, you must distribute the negative sign to each term inside the second parentheses before combining like terms. This ensures correct simplification of the expression.