[tex]\large \bold{\red{given} \begin{cases} \bold {1. ) \: (x+5)(x-2) }\\ \large\bold{2.) \: (2a-b^2)(a+4b^2)} \\ \large \bold{3.) \: (3x + 1)(x {}^{2} - 4x {}^{2} - 7} \\ \large \bold{4.) \: \frac{x {}^{2 - 3x - 10} }{x + 2}} \end{cases}}[/tex]
[tex] \large \bold{SOLUTION:}[/tex]
[tex] \bold{1.) \: ( x+ 5)(x - 2)} \\ \dashrightarrow\bold{(x + 5)(x - 2)} \\ \dashrightarrow \bold{(x)(x)+(x)(−2)+(5)(x)+(5)(−2)} \\ \dashrightarrow \bold{x {}^{2} −2x+5x−10} \\ \large \underline{ \boxed{ \bold{\color{darkviolet} »\: x {}^{2} +3x−10}}}[/tex]
[tex] \bold{2.) \: (2a - b {}^{2} )(a + 4b {}^{2} )} \\ \dashrightarrow \bold{(2a+−b {}^{2} )(a+4b {}^{2} )} \\ \dashrightarrow \bold{(2a)(a)+(2a)(4b {}^{2} )+(−b {}^{2} )(a)+(−b {}^{2} )(4b {}^{2} )} \\ \dashrightarrow \bold{2a {}^{2} +8ab {}^{2} −ab {}^{2} −4b {}^{4} } \\ \large \underline{ \boxed{ \bold{\color{darkviolet} »\: −4b4+7ab2+2a2}}}[/tex]
[tex] \bold{3.) \: (3x + 1)(x {}^{2} - 4x {}^{2} - 7)} \\ \dashrightarrow \bold{(3x+1)(x {}^{2} +−4x {}^{2} +−7)} \\ \dashrightarrow \bold{(3x)(x {}^{2} )+(3x)(−4x {}^{2} )+(3x)(−7)+(1)(x {}^{2} )+(1)(−4x {}^{2} )+(1)(−7)} \\ \dashrightarrow \bold{=3x {}^{3} −12x {}^{3} −21x+x {}^{2} −4x {}^{2} −7} \\ \large \underline{ \boxed{ \bold{\color{darkviolet} »\: −9x {}^{3} −3x {}^{2} −21x−7}}}[/tex]
[tex] \bold{4.) \: \frac{x {}^{2 - 3x - 10} }{x + 2} } \\ \\ \dashrightarrow \bold{ \frac{x {}^{2 } - 3x - 10}{x + 2} } \\ \\ \dashrightarrow \bold{ \frac{(x {}^{2 } + 2)(x - 5) }{x + 2} } \\ \\ \large \underline{ \boxed{ \bold{\color{darkviolet} »\: x - 5}}}[/tex]
[tex] \huge \color{indigo}{ \bold{Carry\:On\: Latex}}[/tex]
