Question

If 2a+b=3,find the value of 8a³+b³+18ab​

Answer 1

27

Explanation:

A sum of cubes factors as

a³ + b³ = (a + b)(a² - ab + b²)

Factor the sum of cubes 8a³ + b³

8a³ = (2a)³, thus

8a³ + b³

= (2a)³ + b³

= (2a + b)(4a² - 2ab + b²)

We now have the right side as

(2a + b)(4a² - 2ab + b²) + 18ab ← substitute 2a + b = 3

= 3(4a² - 2ab + b²) + 18ab

= 12a² - 6ab + 3b² + 18ab ← collect like terms

= 12a² + 12ab + 3b² ← factor out 3 from each term

= 3(4a² + 4ab + b²) ← perfect square

= 3(2a + b)² ← substitute 2a + b = 3

= 3 × 3²

= 3 × 9

= 27

Answer 2

531.

Explanation:

Let's assume 2(1) + 1 = 3

a = 1 and b = 1

Now we can plug that in

8(1)^3 + (1)^3 + 18(1)(1)

Then we need to multiply together

8^3 + 1^3 + 18

Then do the powers

512 + 1 + 18

Then add them together

531

Hope this helped!