What is expand 1+(a-3b)^3 ?

The solution to expand 1+(a-3b)^3 is 1+a^3-9a^2b+27ab^2-27b^3

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expand 1+(a-3b)^3

expand

1 + (a - 3 b)^{3}

1 + a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}

Solution steps

1 + (a - 3 b)^{3}

Apply Perfect Cube Formula:

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

(a - 3 b)^{3} = a^{3} - 3 a^{2} \cdot 3 b + 3 a (3 b)^{2} - (3 b)^{3}

= 1 + a^{3} - 3 a^{2} \cdot 3 b + 3 a (3 b)^{2} - (3 b)^{3}

Simplify

a^{3} - 3 a^{2} \cdot 3 b + 3 a (3 b)^{2} - (3 b)^{3} : a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}

= 1 + a^{3} - 9 a^{2} b + 27 a b^{2} - 27 b^{3}

- 12 \cdot (- 12)

\frac{( 1.24 \cdot 1 0 ^{2} ) ( 3.6 \cdot 1 0 ^{- 3} )}{1.8 \cdot 10}

cos^{2} (x) + 2 sin^{2} (x)

(2 + 3 x)^{5}

x \cdot (- x^{2})

What is expand 1+(a-3b)^3 ?
The solution to expand 1+(a-3b)^3 is 1+a^3-9a^2b+27ab^2-27b^3