Question

factorise:3x^4-6x^2a^2+3a^4​

Answer 1

Answer:

$= > 3 {x}^{4} - 6 {x}^{2} {a}^{2} + 3 {a}^{4} \\ \\ = > 3 {x}^{4} - (3 + 3) {x}^{2} {a}^{2} + 3 {a}^{4} \\ \\ = > 3 {x}^{4} - 3 {x}^{2} {a}^{2} - 3 {x}^{2} {a}^{2} + 3 {a}^{4} \\ \\ = > 3 {x}^{2} ( {x}^{2} - {a}^{2} ) - 3 {a}^{2} ( {x}^{2} - {a}^{2} ) \\ \\ = > ( {x}^{2} - {a}^{2} )(3 {x}^{2} - 3 {a}^{2} ) \\ \\ = > 3( {x}^{2} - {a}^{2} )( {x}^{2} - {a}^{2} ) \\ \\ = > 3 {( {x}^{2} - {a}^{2} )}^{2} \\ \\ = > 3{(x - a)}^{2}{(x + a)}^{2}$

Answer 2

$\huge\star\underline\textsf{Question:- }$

$\star\boxed{\sf3x {}^{4 } - 6x {}^{2} a {}^{2} + 3a {}^{4} }$

$\huge\star\underline\textsf{Explanation:- }$

$\leadsto\sf\green{3x {}^{4} - (3 + 3)x {}^{2} a {}^{2} + 3a {}^{4}}$

$\leadsto\sf\red{3x {}^{4} - 3x {}^{2} {a}^{2} - 3x {}^{2}a {}^{2} + 3a {}^{4} }$

$\leadsto\sf\orange{3x {}^{2} (x {}^{2} - a {}^{2} ) - 3a {}^{2} (x {}^{2} - a {}^{2} )}$

$\leadsto\sf\blue{(x {}^{2} - a {}^{2} )(3x {}^{2} - 3a {}^{2} )}$

$\leadsto\sf\purple{3(x {}^{2} - a {}^{2} )(x {}^{2} - a {}^{2} )}$

$\huge\star\boxed{\bf Ans.3(x {}^{2} - a {}^{2} ) {}^{2} }$