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zubka84 [21]
3 years ago
14

Determine whether 81a2 − 25z6 is a difference of two squares. If so, factor it. If not, explain why.

Mathematics
1 answer:
aev [14]3 years ago
7 0

81 a² - 25 z^{6} is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)

Step-by-step explanation:

The difference of two squares is a binomial of two terms each term is a square and the sign between the two terms is (-), its factorization is the product of two identical binomials with different middle signs

  • a² - b² is a difference of two squares
  • a² - b² = (a + b)(a - b)

∵ The binomial is 81 a² - 25 z^{6}

∵ \sqrt{81} = 9

∵ \sqrt{a^{2} } = a

∴ \sqrt{81a^{2}}=9a

∵ \sqrt{25} = 5

∵ \sqrt{z^{6}} = z³

∴ \sqrt{25z^{6}}=5z^{3}

- The two terms have square root

∵ The sign between them is (-)

∴ 81 a² - 25 z^{6}  is a difference of two squares

∵ Its factorization is two identical brackets with different

   middle signs

∵ 81 a² = 9a × 9a

∵ 25 z^{6} = 5z³ × 5z³

- The terms of the two brackets are 9a and 5z³

∴ 81 a² - 25 z^{6} = (9a + 5z³)(9a - 5z³)

81 a² - 25 z^{6} is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)

Learn more:

You can learn more about the difference of two squares in brainly.com/question/1414397

#LearnwithBrainly

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