Question

66(y^4-5y^3-24y^2)/6y(y-8) Explain with steps

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$ = 11y(y+3)

Step-by-step explanation:

Required to simplify the expression

$\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$

Solution:

Given expression is $\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$

Taking common factor 'y²' in the numerator we get

$\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$  = $\frac{66y^2(y^2-5y-24)}{6y(y-8) }$

Cancel '6y' from the numerator and denominator

$\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$ = $\frac{11y(y^2-5y-24)}{(y-8) }$

Now factorize the quadratic polynomial y² - 5y-24

y² - 5y-24 = y² - 8y+3y-24

= y(y-8)+3(y-8)

= (y+3)(y-8)

y² - 5y-24 = (y+3)(y-8)

Substituting the value of y² - 5y - 24 we get,

$\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$ =  $\frac{11y(y^2-5y-24)}{(y-8) }$

=$\frac{11y(y+3)(y-8)}{(y-8) }$

Cancelling (y-8) from numerator and denominator we get

= 11y(y+3)

Hence we have

$\frac{66(y^4-5y^3-24y^2)}{6y(y-8) }$ = 11y(y+3)

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