[tex] \huge\bf \pink {\underline{Solution :-}}[/tex]
[tex]2 {a}^{2} + 7a - 15[/tex]
[tex] = 2 {a}^{2} + 10a - 3a - 15[/tex]
[tex] = 2a(a + 5) - 3(a + 5)[/tex]
[tex] = (a + 5)(2a - 3)[/tex]
[tex] \sf \red{Hence, Answer \: is \: (a + 5)(2a - 3).}[/tex]
[tex] \\ [/tex]
[tex] \bf \purple{ \underline{ Important \: Formulas \: for \: Factorization :-}}[/tex]
[tex]• \: {a}^{2} + 2ab + {b}^{2} = {(a + b)}^{2} [/tex]
[tex]• \: (a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
[tex]• \: {a}^{2} - 2 ab + {b}^{2} = {(a - b)}^{2} [/tex]
[tex]• \: {a}^{3} + 3 {a}^{2} b + 3a {b}^{2} + {b}^{3} = {(a + b)}^{3} [/tex]
[tex]• \: {a}^{3} - 3 {a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{3} [/tex]
[tex]• \: {(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} + {b}^{2} )[/tex]
[tex]• \: {(a + b)}^{2} - {(a - b)}^{2} = 4ab[/tex]
[tex]• \: (a + b)( {a}^{2} -ab + {b}^{2} ) = {a}^{3} + {b}^{3} [/tex]
[tex]• \: (a - b)( {a}^{2} + ab + {b}^{2} ) = {a}^{3} - {b}^{3}[/tex]
[tex]• \: {( \frac{a + b}{2} )}^{2} - ( {\frac{a - b}{2} } )^{2} = ab[/tex]
