Question

find the value of a³-b³/a-b​

Answer 1

Answer:

a³-b³/a-b =(a-b)( a²-b²)/ (a-b)

=(a²-b²) by algebraic identities

=(a+b) (a-b)

Answer 2

Solution:-

This is a very easy Question....it can be solved using Algebric identities

We know,

• (a-b)³=a³-b³-3ab(a-b)

=>(a-b)³+3ab(a-b)=a³-b³

To find:-

$\frac{a {}^{3} - b {}^{3} }{a - b} \: \: \: = \frac{(a-b)³+3ab(a-b)}{a - b}$

Taking (a-b) as common....

$= \frac{(a-b)((a - b)^{2} +3ab)}{a - b}$

(a-b) and (a-b) gets cancelled.....

$= {(a - b)}^{2} + 3ab \\ = {a}^{2} + {b}^{2} - 2ab + 3ab \\ = {a}^{2} + b {}^{2} + ab$

Correct Answer:-

• a²+b²+ab

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$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

•Please see this answer from brainly.in website