What is expand (5e^2-7f^2)(5e^2+7f^3) ?

The solution to expand (5e^2-7f^2)(5e^2+7f^3) is -49f^5+35e^2f^3-35e^2f^2+25e^4

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expand (5e^2-7f^2)(5e^2+7f^3)

expand

(5 e^{2} - 7 f^{2}) (5 e^{2} + 7 f^{3})

- 49 f^{5} + 35 e^{2} f^{3} - 35 e^{2} f^{2} + 25 e^{4}

Solution steps

(5 e^{2} - 7 f^{2}) (5 e^{2} + 7 f^{3})

Apply FOIL method:

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

a = 5 e^{2}, b = - 7 f^{2}, c = 5 e^{2}, d = 7 f^{3}

= 5 e^{2} \cdot 5 e^{2} + 5 e^{2} \cdot 7 f^{3} + (- 7 f^{2}) \cdot 5 e^{2} + (- 7 f^{2}) \cdot 7 f^{3}

Apply minus-plus rules

+ (- a) = - a

= 5 \cdot 5 e^{2} e^{2} + 5 \cdot 7 e^{2} f^{3} - 7 \cdot 5 e^{2} f^{2} - 7 \cdot 7 f^{3} f^{2}

Simplify

5 \cdot 5 e^{2} e^{2} + 5 \cdot 7 e^{2} f^{3} - 7 \cdot 5 e^{2} f^{2} - 7 \cdot 7 f^{3} f^{2} : - 49 f^{5} + 35 e^{2} f^{3} - 35 e^{2} f^{2} + 25 e^{4}

= - 49 f^{5} + 35 e^{2} f^{3} - 35 e^{2} f^{2} + 25 e^{4}

(x, y) \Rightarrow (x + 1, y + 2)

x (x^{2 - x^{- 1}})

(4 e^{2 - 2 t} + 1) (e^{j^{2} πn t})

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

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

What is expand (5e^2-7f^2)(5e^2+7f^3) ?
The solution to expand (5e^2-7f^2)(5e^2+7f^3) is -49f^5+35e^2f^3-35e^2f^2+25e^4