Expand the following using the binomial theorem and pascal’s triangle. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 in the expansion of (3a + 4b)8, which of the following are possible variable terms? explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5

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Step-by-step explanation:

Use formula for the binomial expansion:

Note that

1. For the expression

2. For the expression

3. For the expression

4. For the xpression

5. In the expansion of each term has the degree of 8. Since product has degree 2+3=5, this term is not possible. Since product has degree 1+8=9, this term is not possible. Similarly, term has degree 6+5=11 and is not a term of expansion   Products have degree 8 (5+3=8=4+4=8=1+7), these products are possible terms with corresponding coefficients.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

168

step-by-step explanation:

i am pretty sure that the answer is 168