What is expand (2c+d+e)(2c+d-e) ?

The solution to expand (2c+d+e)(2c+d-e) is -e^2+4c^2+4cd+d^2

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expand (2c+d+e)(2c+d-e)

expand

(2 c + d + e) (2 c + d - e)

- e^{2} + 4 c^{2} + 4 c d + d^{2}

Solution steps

(2 c + d + e) (2 c + d - e)

Distribute parentheses

= 2 c \cdot 2 c + 2 c d + 2 c (- e) + d \cdot 2 c + dd + d (- e) + e 2 c + e d + e (- e)

Apply minus-plus rules

+ (- a) = - a

= 2 \cdot 2 cc + 2 c d - 2 ec + 2 c d + dd - e d + 2 ec + e d - ee

Simplify

2 \cdot 2 cc + 2 c d - 2 ec + 2 c d + dd - e d + 2 ec + e d - ee : - e^{2} + 4 c^{2} + 4 c d + d^{2}

= - e^{2} + 4 c^{2} + 4 c d + d^{2}

\frac{( 2 x + 1 ) ^{3} ( 2 x - 3 ) ^{3}}{( 4 x + 3 ) ^{2} ( x + 1 ) ^{4}}

(- 20 x y^{2} + 6 x) d x + (3 y^{2} - 20 x^{2} y) d y

5 (5 x^{4} + 8 x^{2} - 7)^{4}

\frac{1}{( s - 2 ) ( s ^{2} + 1 )}

(3 x - \frac{2}{x})^{4}

What is expand (2c+d+e)(2c+d-e) ?
The solution to expand (2c+d+e)(2c+d-e) is -e^2+4c^2+4cd+d^2