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statuscvo [17]
3 years ago
9

Factor completely: A) 64x²-49y² B) 20x²-45y²

Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
8 0

A) This is a difference of two squares. So your equation (a²x² - b²x²) where a and b can be square-rooted ends up being factored to (ax -by)(ax + by).

64x² - 49y² = (8x - 7y)(8x + 7y)

B) Factor out a GCF of 5 from both terms, then you have the same situation as equation A.

20x² - 45y² = 5(4x² - 9y²) = 5(2x - 3y)(2x + 3y)

tigry1 [53]3 years ago
3 0

Use\\a^2-b^2=(a-b)(a+b)\\(ab)^n=a^nb^n\\(\sqrt{a})^2=a\ for\ a\geq0\\------------------------------\\A)\ 64x^2-49y^2=8^2x^2-7^2y^2=(8x)^2-(7y)^2=(8x-7y)(8x+7y)\\\\B)\ 20x^2-45y^2=(\sqrt{20})^2x^2-(\sqrt{45})^2y^2=(*)\\\\\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\\\sqrt{45}=\sqrt{9\cdot5}=\sqrt9\cdot\sqrt5=3\sqrt5\\\\(*)=(2\sqrt5x)^2-(3\sqrt5y)^2=(2\sqrt5x-3\sqrt5y)(3\sqrt5x+3\sqrt5y)

or:\\\\20x^2-45y^2=5\cdot4x^2-5\cdot9y^2=5(4x^2-9y^2)=5[(2x)^2-(3y)^2]\\\\=5(2x-3y)(2x+3y)

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Answer:

angle CBE=15 degrees

Step-by-step explanation:

angle ECD is 60 degrees and EC=CD because equilateral triangle

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angle ECD +angle DCB= angle ECB

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since triangle ECB has legs EC and CB  equal in length, then it is an isosceles triangle.

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angle CBE=(180-150)/2

angle CBE=15 degrees

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valina [46]

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