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What number does C3 represent in the expansion $C subscript 0 a to the power of 5 plus C subscript 1 a to the power of 4 b plus C subscript 2 a squared b squared plus C subscript 3 a b cubed plus C subscript 4 b to the power of 4$ ? Explain.

hint Hint:

The binomial expansion is $left parenthesis x plus y right parenthesis to the power of n equals sum from k equals 0 to n of n C subscript k x to the power of n minus k end exponent y to the power of k$ , here n ≥ 0 .
The value of $n C subscript r equals fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction$
We are asked to find what number does C3 represent in the expansion $C subscript 0 a to the power of 5 plus C subscript 1 a to the power of 4 b plus C subscript 2 a squared b squared plus C subscript 3 a b cubed plus C subscript 4 b to the power of 4$ .

The correct answer is: = 4

Step 1 of 2:
The expansion is: $C subscript 0 a to the power of 5 plus C subscript 1 a to the power of 4 b plus C subscript 2 a squared b squared plus C subscript 3 a b cubed plus C subscript 4 b to the power of 4$
Here, C₃ represents the coefficient of ab³ in the expansion.
Step 2 of 2:
The value of n=4, so the value of C₃ is:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 4 C subscript 3 equals fraction numerator 4 factorial over denominator 3 factorial left parenthesis 4 minus 3 right parenthesis factorial end fraction end cell row cell equals fraction numerator 4 factorial over denominator 3 factorial cross times 1 factorial end fraction end cell row cell equals 4 end cell end table$

The value $n C subscript r equals fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction$ is called the combination permutation.

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Can’t find what you’re looking for?

What number does C3 represent in the expansion ? Explain.

The binomial expansion is , here n ≥ 0 .The value of We are asked to find what number does C3 represent in the expansion .

The correct answer is: = 4

Step 1 of 2:The expansion is: Here, C3 represents the coefficient of ab3 in the expansion.Step 2 of 2:The value of n=4, so the value of C3 is:

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What number does C3 represent in the expansion $C subscript 0 a to the power of 5 plus C subscript 1 a to the power of 4 b plus C subscript 2 a squared b squared plus C subscript 3 a b cubed plus C subscript 4 b to the power of 4$ ? Explain.

Explain how to use a polynomial identity to factor . $8 x to the power of 6 minus 27 y cubed$

Explain how to use a polynomial identity to factor . $8 x to the power of 6 minus 27 y cubed$

Use polynomial identities to factor the polynomials or simplify the expressions :
$10 cubed minus 3 cubed$

Use polynomial identities to factor the polynomials or simplify the expressions :
$10 cubed minus 3 cubed$

How are Pascal’s triangle and binomial expansion such as $left parenthesis a plus b right parenthesis to the power of 5$ related?

How are Pascal’s triangle and binomial expansion such as $left parenthesis a plus b right parenthesis to the power of 5$ related?

Explain how to use a polynomial identity to factor $8 x to the power of 6 minus 27 y cubed$ .

Explain how to use a polynomial identity to factor $8 x to the power of 6 minus 27 y cubed$ .

Use polynomial identities to factor the polynomials or simplify the expressions :
$10 cubed plus 5 cubed$

Use polynomial identities to factor the polynomials or simplify the expressions :
$10 cubed plus 5 cubed$

Explain why the middle term $left parenthesis x plus 5 right parenthesis squared$ is 10x.

Explain why the middle term $left parenthesis x plus 5 right parenthesis squared$ is 10x.

Use polynomial identities to factor the polynomials or simplify the expressions :
$9 cubed plus 6 cubed$

Use polynomial identities to factor the polynomials or simplify the expressions :
$9 cubed plus 6 cubed$

Use binomial theorem to expand $left parenthesis 2 c plus d right parenthesis to the power of 6$

Use binomial theorem to expand $left parenthesis 2 c plus d right parenthesis to the power of 6$

Use polynomial identities to factor the polynomials or simplify the expressions :
$open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses$

Use polynomial identities to factor the polynomials or simplify the expressions :
$open parentheses 1 over 16 x to the power of 6 minus 25 y to the power of 4 close parentheses$

Use binomial theorem to expand . $left parenthesis x minus 1 right parenthesis to the power of 7$

Use binomial theorem to expand . $left parenthesis x minus 1 right parenthesis to the power of 7$

Use polynomial identities to factor the polynomials or simplify the expressions :
$64 x cubed minus 125 y to the power of 6$

Use polynomial identities to factor the polynomials or simplify the expressions :
$64 x cubed minus 125 y to the power of 6$

How are Pascal’s triangle and binomial expansion such as (a + b)⁵ related?

How are Pascal’s triangle and binomial expansion such as (a + b)⁵ related?

Use binomial theorem to expand . $open parentheses s squared plus 3 close parentheses to the power of 5$

Use binomial theorem to expand . $open parentheses s squared plus 3 close parentheses to the power of 5$

Use polynomial identities to factor the polynomials or simplify the expressions :
$216 plus 27 y to the power of 12$

Use polynomial identities to factor the polynomials or simplify the expressions :
$216 plus 27 y to the power of 12$