Question

simplify the following ([a-b]^2)([a+b]^2)

Answer 1

${ \pink{ \bold{ \underline{ \underline{Given:-}}}}}$

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

$</p><p>{ \blue{ \bold{ \underline{ \underline{Find:-}}}}}$

Simplify

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

$</p><p>{ \purple{ \bold{ \underline{\underline{Formulas:-}}}}}$

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

$</p><p>{ \green{ \bold{ \underline{ \underline{Solution:-}}}}}$

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

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

$= {a}^{2} + {b}^{2} + {a}^{2} + {b}^{2}$

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

$= 2 {a}^{2} + 2 {b}^{2}$

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Answer 2

Answer:

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Step-by-step explanation:

(a+b)

2

(a−b)

2

{ \blue{ \bold{ \underline{ \underline{Find:-}}}}}

Find:−

Simplify

{(a + b)}^{2} {(a - b)}^{2}(a+b)

2

(a−b)

2

{ \purple{ \bold{ \underline{\underline{Formulas:-}}}}}

Formulas:−

{(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy(x+y)

2

=x

2

+y

2

+2xy

{(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy(x−y)

2

=x

2

+y

2

−2xy

{ \green{ \bold{ \underline{ \underline{Solution:-}}}}}

Solution:−

{( a+b )}^{2} {(a -b )}^{2}(a+b)

2

(a−b)

2

= {a}^{2} + {b}^{2} + 2 ab + {a}^{2} + {b}^{2} - 2 ab=a

2

+b

2

+2ab+a

2

+b

2

−2ab

= {a}^{2} + {b}^{2} + {a}^{2} + {b}^{2}=a

2

+b

2

+a

2

+b

2

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

2

+b

2

)

= 2 {a}^{2} + 2 {b}^{2}=2a

2

+2b

2