Problem preview
A-APR.1 Warmup M3-001-A02-V01

Add, subtract, and multiply polynomials beyond quadratic cases.

Subtract higher-degree polynomials by combining like terms

Problem

Simplify \((4x^4~+~3x^2~-~1)~-~(x^4~-~5x^2~+~7)\).

Big Picture

What this problem is really about

The main challenge is the subtraction sign in front of the second polynomial, because it applies to every term inside those parentheses. We’ll rewrite the subtraction as adding the opposite, then group equal powers and combine their coefficients. Changing all three signs first keeps the later like-term work accurate.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
A-APR.1
Category
Algebra
Domain
Arithmetic with Polynomials and Rational Expressions
Objective
Add, subtract, and multiply polynomials beyond quadratic cases.
Problem type
Subtract higher-degree polynomials by combining like terms