Multiplying Polynomials

Find the product:

\[ (2a - 1)(8a - 5) \]

(2a - 1) (8a - 5)
= {2a(8a - 5)} - {1(8a - 5)}
= 16a² - 10a - 8a + 5
= 16a² - 18a + 5

Answered by tadvisohil886 | 2024-06-10

The product of (2a-1)(8a-5) is 16a² - 18a + 5.
To find the product of (2a-1)(8a-5), we can use the distributive property . This means that we multiply each term in the first polynomial (2a-1) by each term in the second polynomial (8a-5) and then combine like terms.
Applying the distributive property, we have:
(2a-1)(8a-5) = 2a(8a) + 2a(-5) - 1(8a) - 1(-5)
Simplifying this expression , we get:
16a² - 10a - 8a + 5
Combining like terms , we have:
16a² - 18a + 5
Therefore, the product of (2a-1)(8a-5) is 16a² - 18a + 5.
In this case, we multiplied each term of the first polynomial by each term of the second polynomial, resulting in four terms. Then, we combined like terms to simplify the expression. The final product is a quadratic polynomial with a leading coefficient of 16 and terms involving the variable 'a'.
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Answered by rachanavt02 | 2024-06-17

The product of the polynomials ( 2 a − 1 ) ( 8 a − 5 ) is 16 a 2 − 18 a + 5 . This was found using the distributive property by multiplying each term in the first polynomial by each term in the second polynomial, then combining like terms. The final expression reveals a quadratic polynomial in the variable 'a'.
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Answered by rachanavt02 | 2024-09-27