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Nuetrik [128]
1 year ago
7

36a^(4)b^(10)-81a^(16)b^(20) factor the given expression using the difference of squares pls

Mathematics
1 answer:
ozzi1 year ago
5 0

The factorized expression using difference of squares is as follows,

9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

Difference of Squares

Difference of squares is a factorization method where an expression can be factored as (a + b) (a - b) when considered as the difference of two perfect squares,  a²-b². For instance, factoring x²-25 results in (x+5) (x-5). By enlarging the parentheses in (a + b) (a - b), the pattern (a + b) (a - b)=a²-b² is used as the foundation for this technique.

Factorization Using Difference of Squares

Given expression is,

36a⁴b¹⁰ - 81a¹⁶b²⁰

= (6a²b⁵)² - (9a⁸b¹⁰)²

Using square of differences, we have

a² - b² = (a + b) (a - b)

Here, a = 6a²b⁵ and b = 9a⁸b¹⁰

Thus, we get,

(6a²b⁵ + 9a⁸b¹⁰)(6a²b⁵ - 9a⁸b¹⁰)

Further Factorization

We can take out 3 common from both the bracket terms after applying difference of squares

3×3(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

= 9(2a²b⁵ + 3a⁸b¹⁰)(2a²b⁵ - 3a⁸b¹⁰)

Further, we can take out a²b⁵ as common from both the bracket terms

= 9a²b⁵ (2+3a⁶b⁵)(2-3a⁶b⁵)

Learn more about difference of squares here:

brainly.com/question/11801811

#SPJ4

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The length of a rectangular floor is 4 feet longer than its width w. The area of the floor is 525 ft^2. A) Write a quadratic equ
mina [271]

Answer:

x^21x+25x-525-0

x^21x+25x-525-0xx^2 - 3.7_) +5^2

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-21

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21(x+25)-25=-25

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21(x+25)-25=-25x=21

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21(x+25)-25=-25x=21x+25-25=-25

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21(x+25)-25=-25x=21x+25-25=-25x= 21

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21(x+25)-25=-25x=21x+25-25=-25x= 21x= -25

x^21x+25x-525-0xx^2 - 3.7_) +5^2(5^2.x - 3.5^2.7X X 5^2 x(x^2-1-(3.7))+5^2(x-(3.7))=0 x(x-27)+5^2(x-21)-0 (x-21)((x(x-21_) + 5^2(x-21)_)=0 X-21 X-215^2(x-21)(x+5^2)=0(x-21)(x+25)=0X-21=0x+25= 0x-21+21=21(x+25)-25=-25x=21x+25-25=-25x= 21x= -25ensiah193

4 0
2 years ago
PLSSSS HELPPPPPP ME WITH MATHHH
Ivenika [448]

Answer:

x = 62

Step-by-step explanation:

If the triangle has two values that are the same like your 6s that means that they have the same angle, so you take the angle(56 degrees)  and subtract 180 and 56 making 124. You take 124 and divide it by 2. Making x =62.

7 0
2 years ago
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A bowling leagues mean score is 197 with a standard deviation of 12. The scores are normally distributed. What is the probabilit
Bond [772]

Answer:

0.281 = 28.1% probability a given player averaged less than 190.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A bowling leagues mean score is 197 with a standard deviation of 12.

This means that \mu = 197, \sigma = 12

What is the probability a given player averaged less than 190?

This is the p-value of Z when X = 190.

Z = \frac{X - \mu}{\sigma}

Z = \frac{190 - 197}{12}

Z = -0.58

Z = -0.58 has a p-value of 0.281.

0.281 = 28.1% probability a given player averaged less than 190.

8 0
3 years ago
A farmer wants to seed and fence a section of land. Fencing costs $27 per yard. Grass seed costs $2 per square foot. How much do
Lilit [14]

From.the calculated area and perimeter of the field, it will cost the farmer $475740 to fence and seed the pasture.

<h3>What is the area of the field?</h3>

The area of the field is calculated as follows:

Area of square = 450 ft × 450 ft = 202500 square feet

Area of triangle = (450 ft × 120 ft)/2 = 27000 square feet

Area of field = 229500 square feet

Cost of seeding the field = 229500 × $2 = $459000

Perimeter of the field = 450 + 450 + 450 + 255 + 255 = 1860 ft

1 ft = 1/3 yard

1860 ft = 1860 × 1/3 yards = 620 yards

Cost of fencing = 620 × $27 = $16740

Total cost of seeding and fencing = $475200

Therefore, it will cost the farmer $475740 to fence and seed the pasture.

Learn more about area and perimeter at: brainly.com/question/19819849

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Answer:

-40

Step-by-step explanation:

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3 years ago
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