Question

(4a-3b)^3 - (4a+3b)^3
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Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Simplify:

• (4a-3b)^3 - (4a+3b)^3

Solution:

$:\longrightarrow (4a-3b)^3 - (4a+3b)^3 \\:\longrightarrow [(4a-3b)-(4a+3b)][(4a-3b)^2 + (4a-3b)(4a+3b) + (4a+3b)^2] \\:\longrightarrow [4a-3b-4a-3b][(16a^2+9b^2-24ab) + (16a^2-9b^2) + (16a^2+9b^2+24ab)] \\:\longrightarrow (-6b)(16a^2 + 9b^2 - 24ab + 16a^2 - 9b^2 + 16a^2 + 9b^2 + 24ab) \\:\longrightarrow (-6b)(48a^2 + 9b^2) \\:\longrightarrow (-6b)(3)(16a^2 + 3b^2) \\\bf{:\longrightarrow (-18b)(16a^2 + 3b^2)}$

Formula Used:

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

Learn more:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\bf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$