(8x4+2x2−1)+(3x3−5x2+7x+1)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions

In mathematics, simplifying algebraic expressions often involves combining like terms and applying the order of operations (PEMDAS/BODMAS). Let's take a look at the expression:

(8x⁴ + 2x² − 1) + (3x³ − 5x² + 7x + 1)

Step 1: Removing Parentheses

Since we are adding the two expressions, we can simply remove the parentheses:

8x⁴ + 2x² − 1 + 3x³ − 5x² + 7x + 1

Step 2: Combining Like Terms

Identify terms with the same variable and exponent, and combine their coefficients:

• x⁴ terms: 8x⁴
• x³ terms: 3x³
• x² terms: 2x² - 5x² = -3x²
• x terms: 7x
• Constant terms: -1 + 1 = 0

Step 3: Writing the Simplified Expression

Combine the simplified terms in descending order of exponents:

8x⁴ + 3x³ - 3x² + 7x

Therefore, the simplified form of the expression (8x⁴ + 2x² − 1) + (3x³ − 5x² + 7x + 1) is 8x⁴ + 3x³ - 3x² + 7x.