Question

Expand the following (x-2y)^3​. I want the working

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Use Cube of Difference: $\sf{(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}$

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→ Use Multiplication Distributive Property: $\sf{(xy)}^{a}={x}^{a}{y}^{a}(xy)$

$\tt(x-2y)({x}^{2}-2x\times 2y+{2}^{2}{y}^{2})$

$\tt(x-2y)({x}^{2}-2x\times 2y+4{y}^{2})$

→Simplify 2x×2y to 4xy.

$\tt(x-2y)({x}^{2}-4xy+4{y}^{2})$

→ Expand by distributing sum groups.

$\tt x({x}^{2}-4xy+4{y}^{2})-2y({x}^{2}-4xy+4{y}^{2})$

→Expand by distributing terms.

$\tt{x}^{3}-4{x}^{2}y+4x{y}^{2}-2y({x}^{2}-4xy+4{y}^{2})$

→Expand by distributing terms.

$\tt{x}^{3}-4{x}^{2}y+4x{y}^{2}-(2y{x}^{2}-8{y}^{2}x+8{y}^{3})$

→ Remove parentheses.

$\tt{x}^{3}-4{x}^{2}y+4x{y}^{2}-2y{x}^{2}+8{y}^{2}x-8{y}^{3}$

→Collect like terms.

$\tt{x}^{3}+(-4{x}^{2}y-2{x}^{2}y)+(4x{y}^{2}+8x{y}^{2})-8{y}^{3}$

→ Simplify.

$\tt{x}^{3}-6{x}^{2}y+12x{y}^{2}-8{y}^{3}$

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