Verified answer

Given:-

• To expand — (3a - 4b - 3c)²

Using the expansion formulae:-

[tex] \boxed{ \sf{(a + b + c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac }}[/tex]

Where a = 3a, b = (-4b), c = (-3c).

Substituting the values of a, b, and c, we get,

[tex] \rightarrow \sf{(3a - 4b - 3c) {}^{2} }[/tex]

[tex]{ \rightarrow \sf{(3a) {}^{2} + ( - 4b) {}^{2} + ( - 3c) {}^{2} + 2(3a)( - 4b) + 2( - 4b)( - 3c) + 2( - 3c)(3a) }}[/tex]

[tex]{ \rightarrow \sf{9a {}^{2} + 16 {b}^{2} + 9 {c}^{2} + 2( - 12ab) + 2(12bc) + 2( - 9ac) }}[/tex]

[tex]{ \rightarrow \sf{9a {}^{2} + 16 {b}^{2} + 9 {c}^{2} - 24ab+ 24bc - 18ac }}[/tex]

Please swipe >> for a comfortable view.

[tex]~[/tex]

For reference:-

[tex]\: \: \: \: \: \: \footnotesize{\boxed{\boxed{ \begin{array}{cc} \small\underline{\sf{\pmb{{Algebriac \: identities}}}} \\ \\ \: 1)\sf\:(a + b)^2= a^2+ 2ab + b^2\\\\2)\sf\: (a - b)^2 = a^2- 2ab + b^2\:\\ \\ \: 3)\sf\: (a + b)(a - b) = a^2- b^2 \:\\ \\ \: 4)\sf\:(x + a)(x + b) = x^2 + (a + b)x + ab\:\\ \\ \: 5)\sf\: (a + b)^3 = a^3+ 3a^2b + 3ab^2 + b^3\:\\ \\ \: 6)\sf\:(a - b)^3 = a^3 - 3a^2b + 3ab^2 + b^3\:\\ \\\: \end{array}}}}[/tex]

Given:-

• To expand — (3a - 4b - 3c)²

Using the expansion formulae:-

[tex]\boxed{ \sf{(a + b + c) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac }}

[/tex]

Where a = 3a, b = (-4b), c = (-3c).

Substituting the values of a, b, and c, we get,

[tex]→{(3a - 4b - 3c) {}^{2} }[/tex]

[tex](3a)^2 + (- 4b) ^ 2 + (- 3c) ^ 2 + 2(3a)(- 4b) + 2(- 4b)(- 3c) + 2(- 3c)[/tex]

[tex]{ \rightarrow \sf{9a {}^{2} + 16 {b}^{2} + 9 {c}^{2} + 2( - 12ab) + 2(12bc) + 2( - 9ac) }}[/tex]

[tex]{ \rightarrow \sf{9a {}^{2} + 16 {b}^{2} + 9 {c}^{2} - 24ab+ 24bc - 18ac }}[/tex]

Please swipe >> for a comfortable view.

For reference:-

[tex]\: \: \: \: \: \: \footnotesize{\boxed{\boxed{ \begin{array}{cc} \small\underline{\sf{\pmb{{Algebriac \: identities}}}} \\ \\ \: 1)\sf\:(a + b)^2= a^2+ 2ab + b^2\\\\2)\sf\: (a - b)^2 = a^2- 2ab + b^2\:\\ \\ \: 3)\sf\: (a + b)(a - b) = a^2- b^2 \:\\ \\ \: 4)\sf\:(x + a)(x + b) = x^2 + (a + b)x + ab\:\\ \\ \: 5)\sf\: (a + b)^3 = a^3+ 3a^2b + 3ab^2 + b^3\:\\ \\ \: 6)\sf\:(a - b)^3 = a^3 - 3a^2b + 3ab^2 + b^3\:\\ \\\: \end{array}}}}[/tex]