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[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
[tex] \tt{ \left(3x+2 \right) }^{ 2 } -(3x+1)(3x-5)[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \tt{ \left(3x+2 \right) }^{ 2 } -(3x+1)(3x-5)[/tex]
Use binomial theorem [tex]\tt\left(a+b\right)^{2}=a^{2}+2ab+b^{2}[/tex] to expand [tex]\tt\left(3x+2\right)^{2}[/tex].
[tex] \tt \: 9x^{2}+12x+4-\left(3x+1\right)\left(3x-5\right) [/tex]
Use the distributive property to multiply 3x+1 by 3x-5 and combine like terms.
[tex] \tt \: 9x^{2}+12x+4-\left(9x^{2}-12x-5\right) [/tex]
To find the opposite of 9x²-12x-5, find the opposite of each term.
[tex] \tt \: 9x^{2}+12x+4-9x^{2}+12x+5 [/tex]
Cancel 9x² and -9x² to get 0.
[tex] \tt \: 12x+4+12x+5 [/tex]
Combine 12x and 12x to get 24x.
[tex] \tt \: 24x+4+5 [/tex]
Add 4 and 5 to get 9.
[tex] = \boxed{\boxed{ \bf \: 24x + 9}}[/tex]