Perform the indicated operations. (x4−3x2+2)−(−2x4+x2−$$3)(x^4-3x^2$+2) - (-2x^4$+x^2-3)$$

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 62

1장, 문제 62

Perform the indicated operations. $(x^{4} - 3 x^{2} + 2) - (- 2 x^{4} + x^{2} - 3)$

검증된 단계별 안내

Identify the expression to simplify: $(x^4 - 3x^2 + 2) - (-2x^4 + x^2 - 3)$.

Distribute the subtraction sign across the second polynomial, changing the signs of each term inside the parentheses: $(x^4 - 3x^2 + 2) + (2x^4 - x^2 + 3)$.

Group like terms together: $(x^4 + 2x^4) + (-3x^2 - x^2) + (2 + 3)$.

Combine the coefficients of like terms: add the coefficients of $x^4$ terms, $x^2$ terms, and constant terms separately.

Write the simplified expression by putting together the combined terms.

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.

Polynomial Expressions

Polynomial expressions are algebraic expressions consisting of variables raised to whole-number exponents and coefficients. Understanding how to identify terms, degrees, and coefficients is essential for performing operations like addition and subtraction on polynomials.

Subtraction of Polynomials

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms. Careful attention to distributing the negative sign across all terms is crucial to avoid errors.

Combining Like Terms

Combining like terms means adding or subtracting terms that have the same variable raised to the same power. This simplifies the expression and is a key step after performing addition or subtraction of polynomials.

Perform the indicated operations. (x4−3x2+2)−(−2x4+x2−3)(x^4-3x^2+2) - (-2x^4+x^2-3)