Question

(5 - 2a + a²)(4a2 - 3a - 1);? ​

Answer 1

Ответ:

(5 - 2a + a2)(4a2 - 3a - 1) = 5 * (4a2 - 3a - 1) - 2а * (4a2 - 3a - 1) + а2 * (4a2 - 3a -1) = 20а2 - 15а - 5 - 8а3 + 6а2 + 2а + 4а4 - 3а3 - а= 4а4 - (8 + 3)а3 + (20 + 6 -1)а2 - (15 - 2)а - 5 = 4а4 - 11а3 + 25а2 - 13а - 5.

Пояснение: раскрываем скобки и приводим подобные слагаемые.

Answer 2

(5-2а+а²)(4а²-3а-1)= 20а²-15а-5-8а³+6а²+2а+4а⁴-3а³-а²=

=25а²-13а-5-11а³+4а⁴= 4а⁴-11а³+25а²-13а-5

Answer 3

To multiply the two binomials $(5 - 2a + a^2)(4a^2 - 3a - 1)$, you can use the distributive property to combine like terms. Here's how you can do it step by step:

Step 1: Multiply the first term in the first binomial by each term in the second binomial. $(5)(4a^2) = 20a^2$ $(5)(-3a) = -15a$ $(5)(-1) = -5$

Step 2: Multiply the second term in the first binomial by each term in the second binomial. $(-2a)(4a^2) = -8a^3$ $(-2a)(-3a) = 6a^2$ $(-2a)(-1) = 2a$

Step 3: Multiply the third term in the first binomial by each term in the second binomial. $(a^2)(4a^2) = 4a^4$ $(a^2)(-3a) = -3a^3$ $(a^2)(-1) = -a^2$

Step 4: Add up all the products from Steps 1, 2, and 3 to get the final expression: $20a^2 - 15a - 5 - 8a^3 + 6a^2 + 2a + 4a^4 - 3a^3 - a^2$

Now, you can combine like terms by adding or subtracting them: $4a^4 - 8a^3 - 3a^3 + 6a^2 - a^2 + 20a^2 + 2a - 15a - 5$

Simplify further: $4a^4 - 11a^3 + 5a^2 + 2a - 15a - 5$

Finally, you can combine the like terms for a cleaner expression: $4a^4 - 11a^3 + 5a^2 - 13a - 5$

So, $(5 - 2a + a^2)(4a^2 - 3a - 1) = 4a^4 - 11a^3 + 5a^2 - 13a - 5$.