Questions: Multiply. (y+5u-6)(4y-3u+4) Simplify your answer.

Transcript text: Multiply. \[ (y+5 u-6)(4 y-3 u+4) \] Simplify your answer.

Solution

Solution Steps

To multiply and simplify the given polynomial expressions \((y + 5u - 6)(4y - 3u + 4)\), we will use the distributive property (also known as the FOIL method for binomials) to expand the product. This involves multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.

Step 1: Define the Polynomials

We start with the polynomials \( (y + 5u - 6) \) and \( (4y - 3u + 4) \).

Step 2: Multiply the Polynomials

Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial:

\[ (y + 5u - 6)(4y - 3u + 4) = y(4y) + y(-3u) + y(4) + 5u(4y) + 5u(-3u) + 5u(4) - 6(4y) - 6(-3u) - 6(4) \]

Step 3: Combine Like Terms

After performing the multiplication, we combine like terms to simplify the expression:

\[ = 4y^2 - 3yu + 4y + 20yu - 15u^2 + 20u - 24 \]

Combining the like terms results in:

\[ = 4y^2 + (17yu) + (-15u^2) + (38u) - 24 \]