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Aloiza [94]
2 years ago
11

Prove this polynomial identity... (x − y)(x2 + 2xy + y2)

Mathematics
1 answer:
olga nikolaevna [1]2 years ago
6 0
  • <em>Answer:</em>

<em>x³ + x²y - xy² - y³</em>

  • <em>Step-by-step explanation:</em>

<em>Hi there !</em>

<em>(x − y)(x² + 2xy + y²) =</em>

<em>= x(x² + 2xy + y²) - y(x² + 2xy + y²)</em>

<em>= x³ + 2x²y + xy² - x²y - 2xy² - y³</em>

<em>= x³ + x²y - xy² - y³</em>

<em>Good luck !</em>

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Factor 10x3 + 8x2 - 6x.
valkas [14]
We notice a factor of 2x in both 2x(5x^2+4x-3) trial and error (5x-3)(x+1) yeilds 5x^2+2x-3, nope (5x+3)(x-1) yeilds 5x^2-2x-3, nope (5x-1)(x+3) yeilds 5x^2+14x-3, nope (5x+1)(x-3) yeilds 5x^2-14x-3, nope simplest form is 2x(5x^2+4x-3)
6 0
3 years ago
Does anyone know the minim value of the function f(x) =2x^2 -4x -6?. I’m online due to my quarantine and am looking for extra he
navik [9.2K]

Answer:

f(x) = - 8

Explanation:

The given function is

f(x) =2x^2 -4x -6

The first step is to find the derivative of the function. Recall, if

y = ax^b

y' = abx^(b - 1)

Thus,

f'(x) = 4x - 4

We would equate f'(x) to zero and solve for x. We have

4x - 4 = 0

4x = 4

x = 4/4

x = 1

We would substitute x = 1 into the original function and solve for f(x) or y. It becomes

f(1) =2(1)^2 -4(1) - 6 = 2 - 4 - 6

f(1) = - 8

Thus, the minimum value is f(x) = - 8

4 0
1 year ago
Evaluate 5 + b ÷ (11 - 9) for b = 14.
Trava [24]

Answer:

12

Step-by-step explanation:

5 + b ÷ (11 - 9)

Substitute b = 14

5 + 14 ÷ (11 - 9)

Work the order of operations from left to right

Since there are no exponents, parentheses first

5 + 14 ÷ (11 - 9)

5+14  ÷ 2

Then division

5+7

Then addition

12

8 0
3 years ago
Read 2 more answers
What is the numerical value of 3.14159
kow [346]

Answer:

Pi

Step-by-step explanation:

So pi goes on forever but i and guessing you are look for pi, here are the first 100 digits: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679.

3 0
3 years ago
Read 2 more answers
A is a 4x4 matrix and A^2 + 4A - 5I = 0. If det(A+2I)&gt;0, enter det(A+2I)
maw [93]
\mathbf A^2+4\mathbf A-5\mathbf I=0
\implies\mathbf A^2+4\mathbf A+4\mathbf I=(\mathbf A+2\mathbf I)^2=9\mathbf I
\implies\det\bigg((\mathbf A+2\mathbf I)^2\bigg)=\det(9\mathbf I)
\implies\det(\mathbf A+2\mathbf I)^2=9^4\det\mathbf I
\implies\det(\mathbf A+2\mathbf I)=\pm\sqrt{9^4}
\implies\det(\mathbf A+2\mathbf I)=9^2=81

where we take the positive root because we're told that the determinant is positive.
5 0
3 years ago
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