81 a² - 25 [tex]z^{6}[/tex] 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
∵ The binomial is 81 a² - 25 [tex]z^{6}[/tex]
∵ [tex]\sqrt{81}[/tex] = 9
∵ [tex]\sqrt{a^{2} }[/tex] = a
∴ [tex]\sqrt{81a^{2}}=9a[/tex]
∵ [tex]\sqrt{25}[/tex] = 5
∵ [tex]\sqrt{z^{6}}[/tex] = z³
∴ [tex]\sqrt{25z^{6}}=5z^{3}[/tex]
- The two terms have square root
∵ The sign between them is (-)
∴ 81 a² - 25 [tex]z^{6}[/tex] is a difference of two squares
∵ Its factorization is two identical brackets with different
middle signs
∵ 81 a² = 9a × 9a
∵ 25 [tex]z^{6}[/tex] = 5z³ × 5z³
- The terms of the two brackets are 9a and 5z³
∴ 81 a² - 25 [tex]z^{6}[/tex] = (9a + 5z³)(9a - 5z³)
81 a² - 25 [tex]z^{6}[/tex] 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
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