Question

Perform the operation: (2x² - 6x - 5) * (-9x² + 5x - 4).

Answer 1

The solution is -18x⁴ + 64x³ + 7x² - x + 20.

Step-by-step explanation:

To multiply the polynomials (2x² - 6x - 5) and (-9x² + 5x - 4), we can use the distributive property.

Steps to solve:

Distribute the first polynomial: -18x⁴ + 10x³ - 8x² - 6x(-9x² + 5x - 4) - 5(-9x² + 5x - 4)

Distribute the second polynomial: -18x⁴ + 10x³ - 8x² + 54x³ - 30x² + 24x - 5(-9x² + 5x - 4)

Distribute the third polynomial: -18x⁴ + 10x³ - 8x² + 54x³ - 30x² + 24x + 45x² - 25x + 20

Combine like terms: -18x⁴ + 64x³ - 8x² + 7x² + 24x - 25x + 20

Combine like terms: -18x⁴ + 64x³ + 7x² - x + 20

Answer is: -18x⁴ + 64x³ + 7x² - x + 20

Answer 2

To multiply the polynomials (2x² - 6x - 5) and (-9x² + 5x - 4), apply the distributive property to each term, combine like terms, and simplify to get the final result of -18x⁴ + 64x³ + 7x² - x + 20.

Step-by-step explanation:

To perform the multiplication of the polynomials (2x² - 6x - 5) and (-9x² + 5x - 4), we need to use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Let's multiply each term step by step:

1. Multiply 2x² by each term in the second polynomial: (2x²)(-9x²) = -18x⁴, (2x²)(5x) = 10x³, (2x²)(-4) = -8x².
2. Multiply -6x by each term in the second polynomial: (-6x)(-9x²) = 54x³, (-6x)(5x) = -30x², (-6x)(-4) = 24x.
3. Multiply -5 by each term in the second polynomial: (-5)(-9x²) = 45x², (-5)(5x) = -25x, (-5)(-4) = 20.

Now, combine like terms:

-18x⁴ + (10x³ + 54x³) + (-8x² - 30x² + 45x²) + (24x - 25x) + 20 = -18x⁴ + 64x³ + 7x² - x + 20