What is expand (x-7y)^4 ?

The solution to expand (x-7y)^4 is x^4-28x^3y+294x^2y^2-1372xy^3+2401y^4

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expand (x-7y)^4

expand

(x - 7 y)^{4}

x^{4} - 28 x^{3} y + 294 x^{2} y^{2} - 1372 x y^{3} + 2401 y^{4}

Solution steps

(x - 7 y)^{4}

Apply binomial theorem:

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

a = x, b = - 7 y

= i = 0 \sum 4 (i 4) x^{(4 - i)} (- 7 y)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- 7 y)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 7 y)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 7 y)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 7 y)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 7 y)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} (- 7 y)^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 7 y)^{1} : - 28 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 7 y)^{2} : 294 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 7 y)^{3} : - 1372 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 7 y)^{4} : 2401 y^{4}

= x^{4} - 28 x^{3} y + 294 x^{2} y^{2} - 1372 x y^{3} + 2401 y^{4}

- 8 (0.9 w + 6 w - 0.7) - 0.3 w

4 x^{4} - 9 x^{2} - 6 x - 1

(x^{2} - 4 x + 3) (- 2 x)

(- 6)^{2} \cdot (- 6)^{5}

1.00 1^{2}

What is expand (x-7y)^4 ?
The solution to expand (x-7y)^4 is x^4-28x^3y+294x^2y^2-1372xy^3+2401y^4