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Nonamiya [84]
3 years ago
14

Which of the expressions below can be factor using the difference of squares method

Mathematics
1 answer:
Law Incorporation [45]3 years ago
5 0
25x^2 - 64y^2

The first thing you can do is look for a subtraction sign. The word difference implies subtraction, so you can rule out any expressions that add terms. Secondly, you can look for squares. 17x^2 - 23y^2 is a subtraction expression, but 17 and 23 are not squares. However, 25x^2 - 64x^2 is a subtraction expression and its terms are squares. 25 = 5x5, 64 = 8x8. Hope this helps!
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Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

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So now we can right the Pythagorean theorem as follows:

a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0

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Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

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