(3x-5y+4)(9x^2+25y^2+15xy-20y+12x+16)

Jasonbradley

2 min read

·

Jun 16, 2024

37

Share

Expanding the Expression (3x - 5y + 4)(9x^2 + 25y^2 + 15xy - 20y + 12x + 16)

This expression represents the product of two trinomials. To expand it, we can use the distributive property (also known as FOIL for binomials). Here's how:

Step 1: Distribute the first term of the first trinomial

• (3x) * (9x^2 + 25y^2 + 15xy - 20y + 12x + 16)
  • = 27x^3 + 75xy^2 + 45x^2y - 60xy + 36x^2 + 48x

Step 2: Distribute the second term of the first trinomial

• (-5y) * (9x^2 + 25y^2 + 15xy - 20y + 12x + 16)
  • = -45x^2y - 125y^3 - 75xy^2 + 100y^2 - 60xy - 80y

Step 3: Distribute the third term of the first trinomial

• (4) * (9x^2 + 25y^2 + 15xy - 20y + 12x + 16)
  • = 36x^2 + 100y^2 + 60xy - 80y + 48x + 64

Step 4: Combine like terms

Now, we add all the terms we've obtained:

• 27x^3 + 75xy^2 + 45x^2y - 60xy + 36x^2 + 48x
  • 45x^2y - 125y^3 - 75xy^2 + 100y^2 - 60xy - 80y
  • 36x^2 + 100y^2 + 60xy - 80y + 48x + 64

Simplifying the expression by combining like terms:

• 27x^3 - 125y^3 + 72x^2 + 200y^2 - 60xy - 160y + 96x + 64

Therefore, the expanded form of the expression is: 27x^3 - 125y^3 + 72x^2 + 200y^2 - 60xy - 160y + 96x + 64