What is expand 4(y'+k)^2 ?

The solution to expand 4(y'+k)^2 is 4(y')^2+8ky'+4k^2

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expand 4(y'+k)^2

expand

4 (y^{'} + k)^{2}

4 (y')^{2} + 8 k y' + 4 k^{2}

Solution steps

4 (y^{'} + k)^{2}

(y^{'} + k)^{2} = (y^{'})^{2} + 2 k y^{'} + k^{2}

= 4 (k^{2} + 2 k y^{^{'}} + (y^{^{'}})^{2})

= 4 ((y^{^{'}})^{2} + 2 k y^{^{'}} + k^{2})

Distribute parentheses

= 4 (y^{^{'}})^{2} + 4 \cdot 2 y^{^{'}} k + 4 k^{2}

= 4 (y^{^{'}})^{2} + 4 \cdot 2 k y^{^{'}} + 4 k^{2}

Multiply the numbers:

4 \cdot 2 = 8

= 4 (y^{^{'}})^{2} + 8 k y^{^{'}} + 4 k^{2}

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What is expand 4(y'+k)^2 ?
The solution to expand 4(y'+k)^2 is 4(y')^2+8ky'+4k^2