Question

(3xy - 2ab)^3 - (3xy + 2ab)^3

Answer 1

Given: (3xy - 2ab)³ - (3xy + 2ab)³

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$\sf{(3xy - 2ab)^3 - (3xy + 2ab)^3}$

$:\implies \sf{\Big[ (3xy - 2ab) - (3xy + 2ab)\Big] \Big[(3xy - 2ab)^2 + (3xy - 2ab)(3xy + 2ab) + (3xy + 2ab)^2 \Big]}$

$:\implies \; \sf{\Big( \cancel{3xy}-2ab \cancel{-3xy} - 2ab\Big) } \sf{ \Big[ (3xy)^2 - 2(3xy)(2ab) +(2ab)^2 + 9x^2y^2 - 4a^2b^2 + (3xy)^2 + 2(3xy)(2ab)+(2ab)^2\Big]}$

$:\implies \sf{-4ab \Big[9x^2y^2 \cancel{- 12abxy }+ 4a^2b^2 + 9x^2y^2 \cancel{-4a^2b^2} + 9x^2y^2 \cancel{+ 12abxy} + \cancel{4a^2b^2} \Big]}$

$:\implies \; \sf{-4ab \Big( 27x^2y^2 + 4a^2b^2\Big)}$

$:\implies \; \boxed{\sf{\purple{-108abx^2y^2 - 16a^3b^3}}}$

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

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end$

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Answer 2

Answer:

-108x²y²ab-16a³b³

Step-by-step explanation:

the simplest formula which can be used here is-

a³-b³ = (a-b)(a²+b²+ab)

→ (3xy-2ab)³ - (3xy+2ab)³ = (3xy-2ab - 3xy-2ab)(9x²y² + 4a²b² - 12xyab + 9x²y² + 4a²b² + 12 xyab + 9x²y² - 4a²b²)

→ Answer = (-4ab)(27x²y² + 4a²b²)

→ Answer = -108x²y²ab - 16a³b³