Question

Expanded form of (3a-4b)cube

Answer 1

$\huge\underline\mathbb\purple{ANSWER}$

By using identity VII

$(x - y) {}^{3} = {x}^{3} - 3x {}^{2}y + 3xy^{2} - {y}^{3}$

Given-

$(3a - 4p) {}^{3}$

To solve-

Their product

Solution -

$(3a)^{3} - 3(3a)^{2}(4b) +3(3a)(4b)^{2} - {(4b)}^{3}$

$=> 27a^{3} - 108a^{2} b + 144a {b}^{2} - 64b^{3}$

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Some more identities -

$(x + y) {}^{2} = {x}^{2} + 2xy + {y}^{2}$

$(x - y) {}^{2} = {x}^{2} - 2xy + {y}^{2}$

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

$(x + y + z) {}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx$

$(x + a)(x + b) = {x}^{2} + (a + b)x + (a \times b)$

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Answer 2

Answer:

(3a+4b)^3

= 27a^3+64b^3 + 36(3a+4b)

(a-b)^3 = a^3 - b^3 - 3ab(a-b)