Question

(a+b)³+(a-b)³ factorise​

Answer 1

$\large{ \underline{ \underline{ \sf{ \green{Required \: Solution : }}}}}$

Expanding:

(a + b)³ + (a - b)³

$\sf{ ➨~(a^3 +3a^2b+3ab^2+b^3) – (a^3+ 3a^2b+3ab^2+b^3)}$

➨ 6a²b 2b³

➨ 2b (3a² + b²)

If you are allowed complex coefficients this can be broken down into linear factors.

$\longmapsto \tt{2b( \sqrt{3}a + ib)( \sqrt{3}a + ib) }$

Also notice that,

(a + b)³ + (a - b)³ = (b + a)³ - (b - a )³

= 2a (3a² + b²)

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

Note: See this table in brainly.in website