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scZoUnD [109]
4 years ago
9

64a^3 b^3-125c^3 Which algebraic identity is used in this? Answer with steps

Mathematics
1 answer:
abruzzese [7]4 years ago
6 0

Answer:

64a^3b^3-125c^3=(4ab-5c)(16a^2b^2+40abc+25c^2)

Step-by-step explanation:

You have the following polynomial:

64a^3b^3-125c^3

This expression is of the form:

x^3-y^3

that is, a difference between cubes. The factorization of such a polynomial is given by:

x^3-y^3=(x-y)(x^2+2xy+y^2)

You apply the last expression to the polynomial given in the problem. But first you have:

x^3=64a^3b^3\\\\y^3=125c^3\\\\x=4ab\\\\y=5c

finally, you obtain:

64a^3b^3-125c^3=(4ab-5c)((4ab)^2+2(4ab)(5c)+(5c)^2)\\\\64a^3b^3-125c^3=(4ab-5c)(16a^2b^2+40abc+25c^2)

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A line with a slope of the -5 passes through the points (-4, s)and (-7, 6). What is the value of s ?
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