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Sindrei [870]
3 years ago
7

Factor completely, then place the answer in the proper location on the grid. a3 - b3

Mathematics
2 answers:
kirill115 [55]3 years ago
7 0
\bf \textit{difference of cubes}
\\\\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3 
\\\\
a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad
(a-b)(a^2+ab+b^2)= a^3-b^3\\\\
-------------------------------\\\\
a^3-b^3\implies (a-b)(a^2+ab+b^2)
Effectus [21]3 years ago
7 0

Answer:

We have to find the difference of cubes of any two real numbers

a^3-b^3=(a-b)(a^2+ab+b^2)

Verification of the Result

RHS

  =(a-b)(a^2+ab+b^2)\\\\=a \times (a^2+ab+b^2)-b \times (a^2+ab+b^2)\\\\\text{Using Distributive property }\\\\=a^3+a^2b+ab^2-ba^2-ab^2-b^3\\\\ \text{Cancelling like terms}\\\\=a^3-b^3

=LHS

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