Answer:
1. [tex]Turns = 10000[/tex]
2. [tex]2d\²+3d+1 = (2d+1)(d+1)[/tex]
3. [tex]a\²+7ab+10b\² = (a+5b)(a+2b)[/tex]
Step-by-step explanation:
Solving (1):
Given
[tex]Diameter = 63cm[/tex]
Required
Number of times it turns in a distance of 19.8km
First calculate the circumference of the wheel
[tex]C =\pi D[/tex]
[tex]C =\frac{22}{7} * 63cm[/tex]
Convert cm to km
[tex]C =\frac{22}{7} * 0.00063km[/tex]
[tex]C =\frac{22* 0.00063km}{7}[/tex]
[tex]C =\frac{0.01386km}{7}[/tex]
[tex]C =0.00198km[/tex]
The number of turns is:
[tex]Turns = \frac{19.8km}{0.00198km}[/tex]
[tex]Turns = \frac{19.8}{0.00198}[/tex]
[tex]Turns = 10000[/tex]
Solving (2):
[tex]2d\²+3d+1[/tex]
Expand
[tex]2d\²+3d+1 = 2d\²+2d+d+1[/tex]
Factorize:
[tex]2d\²+3d+1 = 2d(d+1)+1(d+1)[/tex]
[tex]2d\²+3d+1 = (2d+1)(d+1)[/tex]
Solving (3):
[tex]a\²+7ab+10b\²[/tex]
Expand
[tex]a\²+7ab+10b\² = a\²+2ab+5ab+10b\²[/tex]
Factorize:
[tex]a\²+7ab+10b\² = a(a+2b)+5b(a+2b)[/tex]
[tex]a\²+7ab+10b\² = (a+5b)(a+2b)[/tex]
