Question

factorize the following expressions y²-18y+81​

Answer 1

Answer:

y square-9y-9y+81

y(y-9)-9(y-9)

(y-9)(y-9)

(y-9)ka holl square

pls mark as brainlst ans and follow I will follow in return

Answer 2

Answer:

Solving y2+18y+81 = 0 by Completing The Square .

Subtract 81 from both side of the equation :

y2+18y = -81

Now the clever bit: Take the coefficient of y , which is 18 , divide by two, giving 9 , and finally square it giving 81

Add 81 to both sides of the equation :

On the right hand side we have :

we have : -81 + 81 or,

$\frac{ - 81}{1} + \frac{81}{1}$

The common denominator of the two fractions is 1

$Adding \: \frac{ - 81}{1} + \frac{81}{1} \: gives \: \frac{0}{1}$

So adding to both sides we finally get :

y2+18y+81 = 0

Adding 81 has completed the left hand side into a perfect square :

y2+18y+81

=> (y+9) • (y+9)

=> (y+9)2

Things which are equal to the same thing are also equal to one another. Since

y2+18y+81 = 0 and

y2+18y+81 = 0 and y2+18y+81 = (y+9)2

then, according to the la.w of transitivity,

w of transitivity, (y+9)2 = 0

w of transitivity, (y+9)2 = 0We'll refer to this Equation as Eq. 3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(y+9)2 is

=> (y+9)

$\frac{2}{2}$

=> (y+9)1

(y+9)1 y+9

Now, applying the Square Root Principle to Eq. 3.2.1 we get:

we get: y+9 = √ 0

Subtract 9 from both sides to obtain:

(y+9)1 y+9Now, applying the Square Root Principle to Eq. 3.2.1 we get: y+9 = √ 0Subtract 9 from both sides to obtain: y = -9 + √ 0

(y+9)1 y+9

The square root of zero is zero

This quadratic equation has one solution only. That's because adding zero is the same as subtracting zero.

The solution is: y = -9