Question
Simplify:
$x^2(x+2 y)(x-3 y)$
$x^2(x+2 y)(x-3 y)$
✓
Answer
To simplify, we will proceed as follows:
$x^2(x+2 y)(x-3 y)$
$=\left[x^2(x+2 y)\right](x-3 y)$
$=\left(x^3+2 x^2 y\right)(x-3 y)$
$=x^3(x-3 y)+2 x^2 y(x-3 y)$
$=x^4-3 x^3 y+2 x^3 y-6 x^2 y^2$
$=x^4-x^3 y-6 x^2 y^2$
Thus, the answer is $x^4-x^3 y-6 x^2 y^2$.
$x^2(x+2 y)(x-3 y)$
$=\left[x^2(x+2 y)\right](x-3 y)$
$=\left(x^3+2 x^2 y\right)(x-3 y)$
$=x^3(x-3 y)+2 x^2 y(x-3 y)$
$=x^4-3 x^3 y+2 x^3 y-6 x^2 y^2$
$=x^4-x^3 y-6 x^2 y^2$
Thus, the answer is $x^4-x^3 y-6 x^2 y^2$.
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Let Reenu type x words in 8 minutes.
Clearly, less number of words will be typed in less time.
So, it is a case of direct proportion.
Now, $\frac{540}{30}=\frac{\text{x}}{8}$
$\Rightarrow\text{x}=\frac{540-8}{30}$
$\text{x}=144$
Therefore, Reenu will type 144 words in 8 minutes.
→| No. of words | 540 | x |
| Times taken (in min) | 30 | 8 |
So, it is a case of direct proportion.
Now, $\frac{540}{30}=\frac{\text{x}}{8}$
$\Rightarrow\text{x}=\frac{540-8}{30}$
$\text{x}=144$
Therefore, Reenu will type 144 words in 8 minutes.