(x^4)(3x^3-2)(4x^2+5x)

Jasonbradley

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Jun 17, 2024

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Multiplying Polynomials: (x^4)(3x^3-2)(4x^2+5x)

This article explores how to multiply the given polynomial expression: (x^4)(3x^3-2)(4x^2+5x).

Understanding the Process

Multiplying polynomials involves applying the distributive property repeatedly. We can approach this problem in two steps:

1. Multiply the first two factors: (x^4)(3x^3-2)
2. Multiply the result from step 1 by the third factor: (result from step 1)(4x^2+5x)

Step 1: (x^4)(3x^3-2)

• Distribute x^4 to each term inside the parentheses:
  • (x^4)(3x^3) + (x^4)(-2)
• Simplify using the rule of exponents (x^m * x^n = x^(m+n)):
  • 3x^(4+3) - 2x^4
  • 3x^7 - 2x^4

Step 2: (3x^7 - 2x^4)(4x^2+5x)

• Distribute each term in the first set of parentheses to both terms in the second set:
  • (3x^7)(4x^2) + (3x^7)(5x) + (-2x^4)(4x^2) + (-2x^4)(5x)
• Simplify using the rule of exponents:
  • 12x^(7+2) + 15x^(7+1) - 8x^(4+2) - 10x^(4+1)
  • 12x^9 + 15x^8 - 8x^6 - 10x^5

Final Result

The simplified form of the given polynomial expression is: 12x^9 + 15x^8 - 8x^6 - 10x^5