Question

Can anyone please factorize the following :

6 (a+b)^2 +5 (a^2-b^2)-6(a-b)^2

Answer 1

Answer:

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

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

So then expand the following

$6 {(a + b)}^{2} = 6( {a}^{2} + {b}^{2} + 2ab) = >$

$6 {(a + b)}^{2} = 6 {a}^{2} + 6 {b}^{2} + 12ab$

$5 {(a - b)}^{2} = 5 {a}^{2} + 5{b}^{2} - 10ab$

So then

$6 {(a + b)}^{2} - 5 {(a - b)}^{2} + 5( {a}^{2} - {b}^{2} )$

$= > 6 {a}^{2} + 6 {b}^{2} + 12ab$

$- 5 {a}^{2} - 5 {b}^{2} + 10ab + 5 {a}^{2} - 5 {b}^{2}$

$= > 6 {a}^{2} - 4 {b}^{2} + 22ab$

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Answer 2

Refer to the attached image ☺️