What is expand (4x+3)^5 ?

The solution to expand (4x+3)^5 is 1024x^5+3840x^4+5760x^3+4320x^2+1620x+243

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expand (4x+3)^5

expand

(4 x + 3)^{5}

1024 x^{5} + 3840 x^{4} + 5760 x^{3} + 4320 x^{2} + 1620 x + 243

Solution steps

(4 x + 3)^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 4 x, b = 3

= i = 0 \sum 5 (i 5) (4 x)^{(5 - i)} \cdot 3^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} \cdot 3^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} \cdot 3^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} \cdot 3^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} \cdot 3^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (4 x)^{1} \cdot 3^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} \cdot 3^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (4 x)^{5} \cdot 3^{0} : 1024 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (4 x)^{4} \cdot 3^{1} : 3840 x^{4}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (4 x)^{3} \cdot 3^{2} : 5760 x^{3}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (4 x)^{2} \cdot 3^{3} : 4320 x^{2}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (4 x)^{1} \cdot 3^{4} : 1620 x

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (4 x)^{0} \cdot 3^{5} : 243

= 1024 x^{5} + 3840 x^{4} + 5760 x^{3} + 4320 x^{2} + 1620 x + 243

\frac{5}{16} \div 10

- \frac{3}{4} + \frac{3}{4}

7 sin^{2} (x) - 7

(x - 11) (x - 3)

5. 7^{2}

What is expand (4x+3)^5 ?
The solution to expand (4x+3)^5 is 1024x^5+3840x^4+5760x^3+4320x^2+1620x+243