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Ronch [10]
3 years ago
7

Expand the equation (p+q)^5

Mathematics
1 answer:
VashaNatasha [74]3 years ago
7 0
(p + q)⁵
(p + q)(p + q)(p + q)(p + q)(p + q)
{[p(p + q) + q(p + q)][p(p + q) + q(p + q)](p + q)}
{[p(p) + p(q) + q(p) + q(q)][p(p) + p(q) + q(p) + q(q)](p + q)}
(p² + pq + pq + q²)(p² + pq + pq + q²)(p + q)
(p² + 2pq + q²)(p² + 2pq + q²)(p + q)
{[p²(p² + 2pq + q²) + 2pq(p² + 2pq + q²) + q²(p² + 2pq + q²)](p + q)}
{[p²(p²) + p²(2pq) + p²(q²) + 2pq(p²) + 2pq(2pq) + 2pq(q²) + q²(p²) + q²(2pq) + q²(q²)](p + q)}
(p⁴ + 2p³q + p²q² + 2p³q + 4p²q² + 2pq³ + p²q² + 2pq³ + q⁴)(p + q)
(p⁴ + 2p³q + 2p³q + p²q² + 4p²q² + p²q² + 2pq³ + 2pq³ + q⁴)(p + q)
(p⁴ + 4p³q + 6p²q² + 4pq³ + q⁴)(p + q)
p⁴(p + q) + 4p³q(p + q) + 6p²q²(p + q) + 4pq³(p + q) + q⁴(p + q)
p⁴(p)+ p⁴(q) + 4p³q(p) + 4p³q(q) + 6p²q²(p) + 6p²q²(q) + 4pq³(p) + 4pq³(q) + q⁴(p) + q⁴(q)
p⁵ + p⁴q + 4p⁴q + 4p³q² + 6p³q² + 6p²q³ + 4p²q³ + 4pq⁴ + pq⁴ + q⁵
p⁵ + 5p⁴q + 10p³q² + 10p²q³ + 5pq⁴ + q⁵
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Centre of circle = (-2, -3)

Equation of the circle:

( x - ( -2) )² + ( y - (-3) )² = (√2/4)²

(x + 2)² + (y + 3)² = 1/8 (Answer D)

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3 years ago
47:47
BARSIC [14]

Sorry, I'm not sure.

I would suggest asking a trusted adult or teacher or redoing the lesson. Cheating isn't a good path: you will not do well in the future if you always search for answers on the internet.

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2 years ago
here are the numbers of 15 people ate out last month. 6,5,5,3,5,4,3,6,4,3,6,5,3,7,6 find the modea of this data set​
Taya2010 [7]

Answer: 3 and 5

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Although it's optional I recommend writing these integers from least to greatest so it will be easier to see what number occurs most frequently.

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8 0
3 years ago
Read 2 more answers
Order of operation with Integers
vovikov84 [41]

Answer:

8

Step-by-step explanation:

<em>we have to follow PEDMAS.</em>

<u>what we have to do in each operation:</u>

Parenthesis ~  100 + 8 to the second power

Exponents ~ 10 to the 2nd power, 8 to the 2nd power, 2 to the 3rd power

Multiplication  ~  none

Division ~  10 to the 2nd power - (100 + 8 to the second power) divided by 2 to the 3rd power

Addition ~ 100 + 8 to the 2nd power

Subtraction ~ 10 to the 2nd power - (100+8 to the second power)

<u>doing the work:</u>

we start with P: but in what we have to do in the Parenthesis, there is an exponent and addition. we do the exponent first. 8 to the second power is 64. now we can add. 100 + 64 = 164.

E: we did the 2nd exponent, but we need the other 2 for later. 10 to the 2nd power is 100, and 2 to the 3rd power is 8.

we can skip M because there isn't any multiplication to do.

D: we have to do 10 to the 2nd power - (100 + 8 to the second power) first. 100-164= 64. now we can devide. 64 devided by 8 = 8

A: we already did the addition in the parenthesis part.

S: we already did the addition in the parenthesis part.

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3 years ago
△ABC has interior angles with measures x°, 90°, and 70°, and △DEF has interior angles with measures y°, 70°, and 20°. Using the
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The letter answer is d
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