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Zinaida [17]
3 years ago
15

Factorise 9w² - 100​

Mathematics
1 answer:
ohaa [14]3 years ago
8 0

Answer:

9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10).

Step-by-step explanation:

Fact:

\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}.

In other words, (a^{2} - b^{2}), the difference of two squares in the form a^{2} and b^{2}, could be factorized into (a - b)\, (a + b).

In this question, the expression (9\, w^{2} - 100) is the difference between two terms: 9\, w^{2} and 100.

  • 9\, w^{2} is the square of 3\, w. That is: (3\, w)^{2} = 9\, w^{2}.
  • On the other hand, 10^{2} = 100.

Hence:

9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}.

Apply the fact that a^{2} - b^{2} = (a - b) \, (a + b) to factorize this expression. (In this case, a = 3\, w whereas b = 10.)

\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}.

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