What is expand (2x^2+3y)^5 ?

The solution to expand (2x^2+3y)^5 is 32x^{10}+240x^8y+720x^6y^2+1080x^4y^3+810x^2y^4+243y^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2x^2+3y)^5

expand

(2 x^{2} + 3 y)^{5}

32 x^{10} + 240 x^{8} y + 720 x^{6} y^{2} + 1080 x^{4} y^{3} + 810 x^{2} y^{4} + 243 y^{5}

Solution steps

(2 x^{2} + 3 y)^{5}

Apply binomial theorem:

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

a = 2 x^{2}, b = 3 y

= i = 0 \sum 5 (i 5) (2 x^{2})^{(5 - i)} (3 y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x^{2})^{5} (3 y)^{0} : 32 x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x^{2})^{4} (3 y)^{1} : 240 x^{8} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x^{2})^{3} (3 y)^{2} : 720 x^{6} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x^{2})^{2} (3 y)^{3} : 1080 x^{4} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x^{2})^{1} (3 y)^{4} : 810 x^{2} y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x^{2})^{0} (3 y)^{5} : 243 y^{5}

= 32 x^{10} + 240 x^{8} y + 720 x^{6} y^{2} + 1080 x^{4} y^{3} + 810 x^{2} y^{4} + 243 y^{5}

\frac{k + 3}{4 k - 2} \cdot (12 k^{2} + 2 k - 4)

(x + 4) (2 x - 3)

What is expand (2x^2+3y)^5 ?
The solution to expand (2x^2+3y)^5 is 32x^{10}+240x^8y+720x^6y^2+1080x^4y^3+810x^2y^4+243y^5