What is expand (a-by)^4dy ?

The solution to expand (a-by)^4dy is a^4dy-4a^3bydy+6a^2b^2y^2dy-4ab^3y^3dy+b^4y^4dy

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expand (a-by)^4dy

expand

(a - b y)^{4} d y

a^{4} d y - 4 a^{3} b y d y + 6 a^{2} b^{2} y^{2} d y - 4 a b^{3} y^{3} d y + b^{4} y^{4} d y

Solution steps

(a - b y)^{4} d y

(a - b y)^{4} = a^{4} - 4 a^{3} b y + 6 a^{2} b^{2} y^{2} - 4 a b^{3} y^{3} + b^{4} y^{4}

= (b^{4} y^{4} - 4 a b^{3} y^{3} + 6 a^{2} b^{2} y^{2} - 4 a^{3} b y + a^{4}) d y

Distribute parentheses

= d y a^{4} + d y (- 4 a^{3} b y) + d y \cdot 6 a^{2} b^{2} y^{2} + d y (- 4 a b^{3} y^{3}) + d y b^{4} y^{4}

Apply minus-plus rules

+ (- a) = - a

= a^{4} d y - 4 a^{3} b y d y + 6 a^{2} b^{2} y^{2} d y - 4 a b^{3} y^{3} d y + b^{4} y^{4} d y

3 (1 - sin (θ))

(x - 1 + 10)^{2} (x - 1 - 10)

(x - 3) 4 - x

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

\frac{10 s + 1}{10 s \times ( 1 + 5 s )}

What is expand (a-by)^4dy ?
The solution to expand (a-by)^4dy is a^4dy-4a^3bydy+6a^2b^2y^2dy-4ab^3y^3dy+b^4y^4dy