Find a · b.
a = −5, 1 / 2 ,
b = −5, 6

a · b  = 28 units

Step-by-step explanation:

Given vectors

a = (-5, 1/2)

b = (-5, 6)

The scalar or dot product of the two vectors, given by a · b is

a · b  = (-5, 1/2) · (-5, 6)

To solve this, multiply the first term in a with the first term in b and add the result to the product of the second term in a and the second term in b. i.e

a · b  = (-5 x -5) +  (1/2 x 6)

a · b  = 25 + 3

a · b  = 28

Therefore, the dot product of a and b is

a · b  = 28 units

2x^2+5x+17

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answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)