Write the following cube in expanded form:
$(7x - 4y)^{3}$
$(7x - 4y)^{3}$
(N/A) To expand $(7x - 4y)^{3}$,we use the algebraic identity: $(a - b)^{3} = a^{3} - b^{3} - 3a^{2}b + 3ab^{2}$.
Here,$a = 7x$ and $b = 4y$.
Substituting these values into the identity:
$(7x - 4y)^{3} = (7x)^{3} - (4y)^{3} - 3(7x)^{2}(4y) + 3(7x)(4y)^{2}$
$= 343x^{3} - 64y^{3} - 3(49x^{2})(4y) + 3(7x)(16y^{2})$
$= 343x^{3} - 64y^{3} - 588x^{2}y + 336xy^{2}$.
Here,$a = 7x$ and $b = 4y$.
Substituting these values into the identity:
$(7x - 4y)^{3} = (7x)^{3} - (4y)^{3} - 3(7x)^{2}(4y) + 3(7x)(4y)^{2}$
$= 343x^{3} - 64y^{3} - 3(49x^{2})(4y) + 3(7x)(16y^{2})$
$= 343x^{3} - 64y^{3} - 588x^{2}y + 336xy^{2}$.
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