Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match each division expression with the correct quotient.

Answer 1

Answer with explanation:

a)

`(16x^2+48x)/(8x)`

Since, both the terms in the numerator have a common factor as: 8x.

Hence, we take out common 8x from the numerator term and hence it could be written as:

`(8x(2x+6))/(8x)`

i.e.

`=2x+6`

b)

`(56x^2-14x)/(7x)`

Since, both the terms in the numerator have a common factor as: 14x.

Hence, we take out common 14x from the numerator term and hence it could be written as:

`=(14x(4x-1))/(7x)\\\\=2(4x-1)\\\\=8x-2`

c)

`((18x^2+15x))/(3x)`

Since, both the terms in the numerator have a common factor as: 3x.

Hence, we take out common 3x from the numerator term and hence it could be written as:

`=(3x(6x+5))/(3x)\\\\=6x+5`

d)

`(20x^2-32x)/(4x)`

Since, both the terms in the numerator have a common factor as: 4x.

Hence, we take out common 4x from the numerator term and hence it could be written as:

`=(4x(5x-8))/(4x)\\\\=5x-8`

Answer 2

`(16x^2+48x)/(8x) = 2x+6\\(56x^2-14x)/(7x) = 8x-2\\(18x^2+15x)/(3x)=6x+5\\(20x^2-32x)/(4x)=5x-8`

Explanation:

We will solve the division one by one:

`(16x^2+48x)/(8x) = (8x(2x+6))/(8x) = 2x+6\\(56x^2-14x)/(7x)=(7x(8x+2))/(7x)=8x+2\\(18x^2+15x)/(3x) =(3x(6x+5))/(3x) = 6x+5\\(20x^2-32x)/(4x)=(4x(5x-8))/(4x)=5x-8`