Rewrite the expression below. -2a( a + b - 5)+ 3 (-5a + 2b) +b (6a + b - 8)

b^2 + 4 a b - 2 b - 2 a^2 + -5 a

Step-by-step explanation:

Simplify the following:

-2 a (a + b - 5) + 3 (2 b - 5 a) + b (6 a + b - 8)

-2 a (-5 + a + b) = 10 a - 2 a^2 - 2 a b:

10 a - 2 a^2 - 2 a b + 3 (2 b - 5 a) + b (6 a + b - 8)

3 (2 b - 5 a) = 6 b - 15 a:

10 a - 2 a^2 - 2 a b + 6 b - 15 a + b (6 a + b - 8)

b (-8 + 6 a + b) = -8 b + 6 a b + b^2:

10 a - 2 a^2 - 2 a b - 15 a + 6 b + -8 b + 6 a b + b^2

Grouping like terms, 10 a - 2 a^2 - 2 a b - 15 a + 6 b - 8 b + 6 a b + b^2 = b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a):

b^2 + (6 a b - 2 a b) + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)

a b 6 + a b (-2) = 4 a b:

b^2 + 4 a b + (6 b - 8 b) - 2 a^2 + (10 a - 15 a)

6 b - 8 b = -2 b:

b^2 + 4 a b + -2 b - 2 a^2 + (10 a - 15 a)

10 a - 15 a = -5 a:

 b^2 + 4 a b - 2 b - 2 a^2 + -5 a

add an image

step-by-step explanation:

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°