Question

Factorize 2a^2+7a-15​

Answer 1

2a^2+10a-3a-15

2a(a+5)-3(a+5)

(2a-3) (a+5)

Answer 2

`\huge\bf \pink {\underline{Solution :-}}`

`2 {a}^(2) + 7a - 15`

`= 2 {a}^(2) + 10a - 3a - 15`

`= 2a(a + 5) - 3(a + 5)`

`= (a + 5)(2a - 3)`

`\sf \red{Hence, Answer \: is \: (a + 5)(2a - 3).}`

`\\`

`\bf \purple{ \underline{ Important \: Formulas \: for \: Factorization :-}}`

`• \: {a}^(2) + 2ab + {b}^(2) = {(a + b)}^(2)`

`• \: (a + b)(a - b) = {a}^(2) - {b}^(2)`

`• \: {a}^(2) - 2 ab + {b}^(2) = {(a - b)}^(2)`

`• \: {a}^(3) + 3 {a}^(2) b + 3a {b}^(2) + {b}^(3) = {(a + b)}^(3)`

`• \: {a}^(3) - 3 {a}^(2) b + 3a {b}^(2) - {b}^(3) = {(a - b)}^(3)`

`• \: {(a + b)}^(2) + {(a - b)}^(2) = 2( {a}^(2) + {b}^(2) )`

`• \: {(a + b)}^(2) - {(a - b)}^(2) = 4ab`

`• \: (a + b)( {a}^(2) -ab + {b}^(2) ) = {a}^(3) + {b}^(3)`

`• \: (a - b)( {a}^(2) + ab + {b}^(2) ) = {a}^(3) - {b}^(3)`

`• \: {( (a + b)/(2) )}^(2) - ( {(a - b)/(2) } )^(2) = ab`