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blondinia [14]
3 years ago
6

Factor 2x2c2 + 3xc2 − 35c2. Show your work.

Mathematics
2 answers:
Feliz [49]3 years ago
6 0

\\ \sf\longmapsto 2x^2c^2+3xc^2-35c^2

  • Take c^2 common

\\ \sf\longmapsto c^2(2x^2+3x-35)

  • Factor the brackets

\\ \sf\longmapsto c^2(2x^2+10x-7x-35)

\\ \sf\longmapsto c^2(2x(x+5)-7(x+5))

\\ \sf\longmapsto c^2(2x-7)(x+5)

Dimas [21]3 years ago
3 0

Answer:

  • c²(x + 5)(2x - 7)

Step-by-step explanation:

  • 2x²c² + 3xc² - 35c² =
  • c²(2x² + 3x - 35) =
  • c²(2x² + 10x - 7x - 35) =
  • c²(2x(x + 5) - 7(x + 5)) =
  • c²(x + 5)(2x - 7)
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How many solutions does these equations have? One, infinite or no solutions?
s2008m [1.1K]

Answer:

  • 1. 7(y + 3) = 5y+8: <u>one solution</u>

  • 2. 10 + 6x= 2(5+3x): <u>infinite solutions</u>

  • 3. 3x + 5 - x=2x + 7: <u>no solutions</u>

  • 4. 4x - 4 = 2x + 8: <u>one solution.</u>

Explanation:

<u>1. 7(y+3)=5y+8</u>

<u></u>

a)  Distributive property of multiplication over addtion:

  • 7y + 21 = 5y + 8

b) Subtraction property of equalities:

  • 7y - 5y = 8 - 21

c) Combine like terms:

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d) Division property of division:

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e) Conclusion: the equation has one solution.

<u>2. 10 + 6x = 2(5+3x)</u>

a) Distributive property of multiplication over addition:

  • 10 + 6x = 10 + 6x

b) Subtraction property of equality:

  • 6x - 6x = 10 - 10

c) Simplify (combine like terms)

  • 0 = 0

That is an identity, i.e. that is always true, no matter the value of x.

d) Conclusion: the equation has infinite solutions.

<u>3. 3x + 5 - x = 2x + 7</u>

a) Combine like terms:

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b) Subtraction property of equalities:

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c) Combine like terms (simplify)

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d) Conclusion: the equation does not have any solutions.

<u>4. 4x - 4 = 2x + 8</u>

<u></u>

a) Subtraction property of equality

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b) Combine like terms

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c) Addtiion property of equalities:

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d) Combine like terms (simplify)

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e) Division property of equalities:

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f) Conclusion: the equation has one solution

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