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Answer :
The correct simplification of (5x³ − 5x − 8) (2x³+4x+2) is given by the option 3 which is 3x³ + 9x - 10
A polynomial is a mathematical expression consisting of different variables and coefficients.
When two or more polynomials are multiplied together, they are referred to as polynomial multiplication.
The result of polynomial multiplication is yet another polynomial.
The method of multiplying polynomials is similar to that of multiplying two numbers with each other.
To complete this multiplication, the distributive property must be used to multiply each term of one polynomial by each term of the other.
Furthermore, combining like terms is an important aspect of simplifying the product obtained by polynomial multiplication.
For the given question, we have: (5x³ − 5x − 8) (2x³ + 4x + 2)
To obtain the product of this multiplication, we must first multiply the first term, 5x³, by each of the three terms in the second polynomial.
This gives us:5x³ x 2x³ + 5x³ x 4x + 5x³ x 2which simplifies to: 10x⁶ + 20x⁴ + 10x³
Next, we multiply the second term, -5x, by each of the three terms in the second polynomial:
-5x³ x 2x³ - 5x x 4x - 5x x 2
which gives us: -10x⁴ - 20x² - 10x
Finally, we multiply the third term, -8, by each of the three terms in the second polynomial:
-8 x 2x³ - 8 x 4x - 8 x²
which gives us: -16x³ - 32x - 16
Now we can combine the like terms obtained above.
The final result of the multiplication is:10x6 - 10x4 - 6x³ - 32x - 16 which simplifies to: 3x³ + 9x - 10
Thus, the correct answer is 3x³ + 9x - 10.
To learn more about polynomial
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