Question

(x+3y)² + (3x + y ) ² simplify the following​

Answer 1

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Answer 2

Answer:

$\boxed{2(5 {x}^{2} + 6xy + 5 {y}^{2} ) }$

Step-by-step explanation:

$= > {(x + 3y)}^{2} + {(3x + y)}^{2} \\ \\ = > ( {x}^{2} + 2(x)(3y) + {(3y)}^{2} ) + ( {(3x)}^{2} + 2(3x)(y) + {y}^{2} ) \\ \\ = > {x}^{2} + 6xy + {9y}^{2} + 9 {x}^{2} + 6xy + {y}^{2} \\ \\ = > {x}^{2} + 9 {x}^{2} + {9y}^{2} + {y}^{2} + 6xy + 6xy \\ \\ = > 10 {x}^{2} + 10 {y}^{2} + 12xy \\ \\ = > 2(5 {x}^{2} + 5 {y}^{2} + 6xy) \\ \\ = > 2(5 {x}^{2} + 6xy + 5 {y}^{2} )$

Additional information:

Algebraic Formulae:

${(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ \\ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} \\ \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ { (a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ac) \\ \\ {(a + b)}^{2} + {(a - b)}^{2} = 2( {a}^{2} - {b}^{2} ) \\ \\ {(a + b)}^{2} - {(a - b)}^{2} = 4ab \\ \\ {(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ {(a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \\ \\ {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} ) \\ \\ {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ \\ {a}^{3} + {b}^{3} + {c}^{3} = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac) + 3abc$