Answer:
[{3y(y-6)}/{2(y-8)}]
Step-by-step explanation:
Given expression is [{45y³(y²+2y-48)}/{30y²(y²-64)}]
Now, in numerator
y² + 2y - 48
= y² + 8x -6x - 48
= y(y + 8) - 6(y + 8)
⇛y² + 2y - 48 = (y-6)(y+8)
Next, in denominator
y² - 64
= y² - 8²
= (y - 8)(y + 8)
Consider,
[{45y³(y²+2y-48)}/{30y²(y²-64)}]
= [{(3*3*3)y³(y-6)(y+8)}/{(2*3*5)y²(y-8)(y+8)}]
= [{3y(y-6)}/{2(y-8)}]
⇛[{45y³(y²+2y-48)}/{30y²(y²-64)}] = [{3y(y-6)}/{2(y-8)}] Ans.
Please let me know if you have any other questions.
[tex] \frac{ {45y}^{3}( {y}^{2} + 2y - 48) }{ {30y}^{2} ( {y}^{2} - 64) } [/tex]
[tex] = \frac{ {45y}^{3}( {y}^{2} + 8y - 6y - 48)}{ {30y}^{2} ( {(y)}^{2} - {(8)}^{2} } ) \\ = \frac{ {45y}^{3}( y(y + 8)- 6(y + 8)}{ {30y}^{2}(y - 8)(y + 8)} \\ = \frac{ {45y}^{3}( y - 6)(y + 8)}{ {30y}^{2}(y - 8)(y + 8)} \\[/tex]
[tex] = \frac{45 {y}^{3}(y - 6) }{30 {y}^{2} (y - 8)} [/tex]
[tex] = \frac{3y(y - 6)}{2(y - 8)} [/tex]
Answer:
[tex] \frac{3y(y - 6)}{2(y - 8)} [/tex]
Hope you could understand.
If you have any query, feel free to ask.
