Convert between numbers and words for large Indian numbering system values and perform polynomial division.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the math problems.

Q1. Write in words / Write in numbers:

Q2. Divide:

Divide each term in the numerator by the denominator.
$\frac{25m^4 - 15m^3}{5m} = \frac{25m^4}{5m} - \frac{15m^3}{5m}$
Simplify each term using the exponent rule $\frac{a^x}{a^y} = a^{x-y}$ .
$\frac{25m^4}{5m} = 5m^{4-1} = 5m^3$ $\frac{15m^3}{5m} = 3m^{3-1} = 3m^2$
Combine the simplified terms.
$5m^3 - 3m^2$
The final answer is $\boxed{5m^3 - 3m^2}$ .
1. $(y^3 + 0y^2 + 0y + 216) \div (y+6)$
Recognize the numerator as a sum of cubes, $y^3 + 216$ .
Note that $216 = 6^3$ .
So, the expression is $y^3 + 6^3$ .
Apply the sum of cubes formula
$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$ .
Here, $a=y$ and $b=6$ .
$y^3 + 6^3 = (y+6)(y^2 - (y)(6) + 6^2)$ $y^3 + 6^3 = (y+6)(y^2 - 6y + 36)$
Substitute this back into the division problem.
$\frac{(y+6)(y^2 - 6y + 36)}{(y+6)}$
Cancel out the common factor $(y+6)$ from the numerator and denominator.
$y^2 - 6y + 36$
The final answer is $\boxed{y^2 - 6y + 36}$ .

Step-by-step solution