Question

If p = 2q +6, then what is the value
of p^3 - 8p^3 - 36pq - 216 ?​

Answer 1

$If \:p = 2q + 6 , then$

The value of p³ - 8p³ - 36pq - 216

= ( 1 - 8 )p³ - 36pq - 216

= -7p³ - 36pq - 216

= -7( 2q + 6 )³ - 36( 2q + 6 ) q - 216

= -7 [ (2q)³ + 3×(2q)²×6 + 3×2q×6²+6³]-72q²-216q-216

= -7( 8q³+72q²+216q+216) -72q²-216q-216

= - 56q³ - 504q² - 1512q - 1512 - 72q²-216q-216

= -56q³ - (504+72)q²-(1512+216)q-(1512+216)

= -56q³ - 576q² - 1728

Therefore.,

$\red{ Value \:of \:p^{3}-8p^{3}-36pq-216}$

$\green { -56q^{3}-576q^{2}-1728}$

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Answer 2

Answer:

The value of p³ - 8p³ - 36pq - 216

= ( 1 - 8 )p³ - 36pq - 216

= -7p³ - 36pq - 216

= -7( 2q + 6 )³ - 36( 2q + 6 ) q - 216

= -7 [ (2q)³ + 3×(2q)²×6 + 3×2q×6²+6³]-72q²-216q-216

= -7( 8q³+72q²+216q+216) -72q²-216q-216

= - 56q³ - 504q² - 1512q - 1512 - 72q²-216q-216

= -56q³ - (504+72)q²-(1512+216)q-(1512+216)

= -56q³ - 576q² - 1728

Therefore.,

Step-by-step explanation: