What is expand (d^2e^3f^4-3)(d^2e^3f^4+5) ?

The solution to expand (d^2e^3f^4-3)(d^2e^3f^4+5) is e^6d^4f^8+2e^3d^2f^4-15

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expand (d^2e^3f^4-3)(d^2e^3f^4+5)

expand

(d^{2} e^{3} f^{4} - 3) (d^{2} e^{3} f^{4} + 5)

e^{6} d^{4} f^{8} + 2 e^{3} d^{2} f^{4} - 15

Solution steps

(d^{2} e^{3} f^{4} - 3) (d^{2} e^{3} f^{4} + 5)

= (e^{3} d^{2} f^{4} - 3) (e^{3} d^{2} f^{4} + 5)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = d^{2} e^{3} f^{4}, b = - 3, c = d^{2} e^{3} f^{4}, d = 5

= d^{2} e^{3} f^{4} d^{2} e^{3} f^{4} + d^{2} e^{3} f^{4} \cdot 5 + (- 3) d^{2} e^{3} f^{4} + (- 3) \cdot 5

Apply minus-plus rules

+ (- a) = - a

= e^{3} e^{3} d^{2} d^{2} f^{4} f^{4} + 5 e^{3} d^{2} f^{4} - 3 e^{3} d^{2} f^{4} - 3 \cdot 5

Simplify

e^{3} e^{3} d^{2} d^{2} f^{4} f^{4} + 5 e^{3} d^{2} f^{4} - 3 e^{3} d^{2} f^{4} - 3 \cdot 5 : e^{6} d^{4} f^{8} + 2 e^{3} d^{2} f^{4} - 15

= e^{6} d^{4} f^{8} + 2 e^{3} d^{2} f^{4} - 15

e^{t - 2} h (t - 2)

(x - 2) (x - 2)

- \frac{s}{2 ( s ^{2} + 8 s + 16 )}

4.9 (5 - \frac{s}{340})^{2}

f (x) = (e^{x} + e^{- x})^{4}

What is expand (d^2e^3f^4-3)(d^2e^3f^4+5) ?
The solution to expand (d^2e^3f^4-3)(d^2e^3f^4+5) is e^6d^4f^8+2e^3d^2f^4-15