Question

Write a algebraic expression

1. The product of the third power of a and The fourth power of b

2. Six less than three times the square of Y

3. The sum of a and b increase by the quotient of b and a

4. Four times the sum of r and a increased by twice the different r and s

5. Triple the difference of 55 and cube of w

Answer 1

1.
`a^(3)b^(4)`.

2.
`3Y^(2) - 6`.

3.
`a + b + (b)/(a)`.

4.
`4(r + a) + 2(r - s)`.

5.
`3(55 - w^(3))`.

Explanation:

1. The product of the third power of a and the fourth power of b =
`a^(3)b^(4)`.

The 'third power of a' means 'a to the power 3' and 'fourth power of b' means 'b to the power 4'.

2. Six less than three times the square of Y means
`3Y^(2) - 6`.

Here, 'three times the square of Y' means 'product of 3 and Y to the power 2', and 'six less than' means 'subtract 6 from the expression'.

3. The sum of a and b increase by the quotient of b and a means
`a + b + (b)/(a)`.

Here, 'quotient of b and a' means 'b divided by a'.

4. Four times the sum of r and a increased by twice the different r and s means
`4(r + a) + 2(r - s)`.

Here, 'increased by' means 'addition' and 'different r and s' means 'r minus s'.

5. Triple the difference of 55 and cube of w means
`3(55 - w^(3))`.

Here, triple means 3 times. (Answer)