Question

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

Answer 1

Answer:

$\frac{16x^2+48x}{8x} = 2x+6\\\frac{56x^2-14x}{7x} = 8x-2\\\frac{18x^2+15x}{3x}=6x+5\\\frac{20x^2-32x}{4x}=5x-8$

Step-by-step explanation:

We will solve the division one by one:

$\frac{16x^2+48x}{8x} = \frac{8x(2x+6)}{8x} = 2x+6\\\frac{56x^2-14x}{7x}=\frac{7x(8x+2)}{7x}=8x+2\\\frac{18x^2+15x}{3x} =\frac{3x(6x+5)}{3x} = 6x+5\\\frac{20x^2-32x}{4x}=\frac{4x(5x-8)}{4x}=5x-8$

Answer 2

Answer with explanation:

a)

$\dfrac{16x^2+48x}{8x}$

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:

$\dfrac{8x(2x+6)}{8x}$

i.e.

$=2x+6$

b)

$\dfrac{56x^2-14x}{7x}$

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:

$=\dfrac{14x(4x-1)}{7x}\\\\=2(4x-1)\\\\=8x-2$

c)

$\dfrac{(18x^2+15x)}{3x}$

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:

$=\dfrac{3x(6x+5)}{3x}\\\\=6x+5$

d)

$\dfrac{20x^2-32x}{4x}$

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:

$=\dfrac{4x(5x-8)}{4x}\\\\=5x-8$