What is expand (2n^3+5re^4)(2n^3+5r^4) ?

The solution to expand (2n^3+5re^4)(2n^3+5r^4) is 4n^6+10n^3r^4+10e^4n^3r+25e^4r^5

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expand (2n^3+5re^4)(2n^3+5r^4)

expand

(2 n^{3} + 5 r e^{4}) (2 n^{3} + 5 r^{4})

4 n^{6} + 10 n^{3} r^{4} + 10 e^{4} n^{3} r + 25 e^{4} r^{5}

Solution steps

(2 n^{3} + 5 r e^{4}) (2 n^{3} + 5 r^{4})

= (2 n^{3} + 5 e^{4} r) (2 n^{3} + 5 r^{4})

Apply FOIL method:

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

a = 2 n^{3}, b = 5 r e^{4}, c = 2 n^{3}, d = 5 r^{4}

= 2 n^{3} \cdot 2 n^{3} + 2 n^{3} \cdot 5 r^{4} + 5 r e^{4} \cdot 2 n^{3} + 5 r e^{4} \cdot 5 r^{4}

= 2 \cdot 2 n^{3} n^{3} + 2 \cdot 5 n^{3} r^{4} + 5 \cdot 2 e^{4} n^{3} r + 5 \cdot 5 e^{4} r^{4} r

Simplify

2 \cdot 2 n^{3} n^{3} + 2 \cdot 5 n^{3} r^{4} + 5 \cdot 2 e^{4} n^{3} r + 5 \cdot 5 e^{4} r^{4} r : 4 n^{6} + 10 n^{3} r^{4} + 10 e^{4} n^{3} r + 25 e^{4} r^{5}

= 4 n^{6} + 10 n^{3} r^{4} + 10 e^{4} n^{3} r + 25 e^{4} r^{5}

(π (r + 3)^{2}) - (π \cdot r^{2})

\frac{d ^{2}}{d x ^{2}} ((2 x^{2} - 1) e^{- x^{2}}) + 5

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

6 (9 + 2)

\frac{( π \cdot ( 3 \cdot x - 3 x ) )}{3}

What is expand (2n^3+5re^4)(2n^3+5r^4) ?
The solution to expand (2n^3+5re^4)(2n^3+5r^4) is 4n^6+10n^3r^4+10e^4n^3r+25e^4r^5