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

Step-by-step explanation:

 Using the binomial theorem,

and

Using pascal's triangle, From the given picture,

a=x, b=2 and n=6, using the 7th row of pascals triangle,

=

a=x, b=-4 and n=4 and using the 5th row of pascals triangle

a=2x , b=3 and n=5, using the 6th row of pascal's triangle

a=2x, b=-3y, n=4, using the 5th row,

Now, in the expansion of , The degree of the term must add up to 8. is of degre 8 than the other terms, this is because is same as , adding the components 1 and 7, we get 8.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°