Question

6. Write the following cubes in expanded form:

(iii) (3a + 4b)³

8. Evaluate the following cubes using suitable Identities:

(ii) (999)³

​

Answer 1

Explanation:

we can use this algebraic identity:

`(a+b)^(3) =a^(3) +b^(3) +3ab(a+b)`

So,
`(3a+4b)^(3) =(3a)^(3) +(4b)^(3)+3(3a)(4b)(3a+4b)`

=
`(3a+4b)^(3) =27a^(3) +64b^(3) +36ab(3a+4b)`

=
`(3a+4b)^(3) =27a^(3) +64b^(3) +108a^(2) b+144ab^(2)`

`(999)^(3)`=
`(1000-1)^(3)`

Now, we can use the following identity:

`(a-b)^(3) =a^(3) -b^(3) -3ab(a-b)`

=
`(1000-1)^(3) =1000^(3) -1^(3) -3(1000)(1)(1000-1)\\`

`(1000-1)^(3) =1,000,000,000-1-2,997,000`

`(1000-1)^(3) =997,002,999`