Question 1

Factorize 2a^2+7a-15

Question 2

Answer:

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

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

(2a-3) (a+5)

Question 3

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

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

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

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

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

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

$\\$

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

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

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

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

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

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

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

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

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

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

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

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