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FromTheMoon [43]
3 years ago
12

Find the polynomial. (2y − 9)(2y − 9) is the factored form of the expression .

Mathematics
2 answers:
Roman55 [17]3 years ago
7 0
(2y-9)(2y-9)
(2y-9)^2
(2y)^2-2*2y*9+9^2
4y^2-36y+81

ehidna [41]3 years ago
7 0

Answer:

The polynomial whose factored form is  (2y-9)(2y- 9)

is  4y^2+81-36y

Step-by-step explanation:

Given : Factored form of a polynomial as (2y-9)(2y- 9)

We have to find the polynomial whose factored form is  (2y-9)(2y- 9)

Consider the given expression  (2y-9)(2y- 9)

\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}

We have,

\left(2y-9\right)\left(2y-9\right)=\:\left(2y-9\right)^{1+1}=\:\left(2y-9\right)^2

Thus, Applying algebraic identity, (a-b)^2=a^2+b^2-2ab,  we have,

a = 2y and b = 9

Thus,  (2y-9)^2=(2y)^2+9^2-2\cdot 2y \cdot 9

Simplify, we have,

(2y-9)^2=4y^2+81-36y

Thus, The polynomial whose factored form is  (2y-9)(2y- 9)

is  4y^2+81-36y

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as a fraction with a common denominator, multiply by

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9

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4

⋅

9

9

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47

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4

4

4

4

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a

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13

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⋅

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9

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4

a

+

13

4

⋅

9

9

+

47

9

⋅

4

4

Write each expression with a common denominator of

36

36

, by multiplying each by an appropriate factor of

1

1

.

a

+

13

⋅

9

36

+

47

⋅

4

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a

+

13

⋅

9

36

+

47

⋅

4

36

Combine the numerators over the common denominator.

a

+

13

⋅

9

+

47

⋅

4

36

a

+

13

⋅

9

+

47

⋅

4

36

Simplify the numerator.

a

+

305

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a

+

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