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3 years ago

Multiply using the rule for the square of a binomial.

Mathematics

1 answer:

GalinKa [24]3 years ago

5 0

To solve:
(x-10)(x-10)

Answer: x^2-20x+100

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x

= $64 + 192 \times x^{1} + 240 \times x^{2}$ + terms involving higher powers of x

so, the first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

Again,

$(2+x - x^{2})^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})$

Now, by inspection,

the term $x^{2}$ comes from k =5 and k = 6

for k = 5, the coefficient of $x^{2}$ is , $(-32) \times 6$ = -192

for k = 6 , the coefficient of $x^{2}$ is, $6_{C_{2}} \times 2^{4}$ = 240

so, coefficient of $x^{2}$ in the final expression = (240 - 192) = 48

3 0

3 years ago

Anyone have any idea what the pattern may be? Need help ASAP!

Anna007 [38]

Answer:

21, 34, 55

Step-by-step explanation:

13+8=21

21+13=34

34+21=55

4 0

3 years ago

Jared had 75 plants. Nina gave him 96 more. Choose the best way to tell how many plants Jared had. Estimate by rounding each num

coldgirl [10]

Answer:

Anwser is A . i think

Step-by-step explanation

6 0

3 years ago

PLS HELP TIMED QUIZ The size of a television screen is given as the length of the diagonal. If a television is advertised as hav

grin007 [14]

Answer:

D.24

Pythagorean states:

hypotenuse^2 = side1^2 + side2^2

30^2 = 18^2 + side2^2

side2^2 = 30^2 - 18^2

side2^2 = 900 - 324

side2^2 = 576

side2 = sqr root 576

side2 = 24

Source: http://www.1728.org/pythgorn.htm

Step-by-step explanation:

5 0

3 years ago

In the diagram, ∠4 and ∠5 are what type of angles?

igomit [66]

Answer:

B. Alternate interior angles

Step-by-step explanation:

<4 and <5 are inside the parallel lines on alternate sides of the third line.

6 0

3 years ago