(2x+3y+4z)(4x^2+9y^2+16z^2-6xy-12yz-8zx)

1.1 Factoring: 4x2+9y2+16z2-6xy-12yz-8xz

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -6xy-12yz
Group 2: 16z2-8xz
Group 3: 4x2+9y2

Pull out from each group separately :

Group 1: (x+2z) • (-6y)
Group 2: (x-2z) • (-8z)
Group 3: (4x2+9y2) • (1)

Looking for common sub-expressions :

Group 1: (x+2z) • (-6y)
Group 3: (4x2+9y2) • (1)
Group 2: (x-2z) • (-8z)

Use vector addition: wind vector w: direction from = 58 degreesdirection to = 238 degreesmagnitude = 20decompose w into rectangular coordinates: wy = 20cos(58) = 10.598wx = 20sin(58) = 16.961airplane vector a: direction = 180 degreesmagnitude = 288decompose a into rectangular coordinates: ay = 288cos(0) = 288ax = 288sin(0) = 0sum: sy = ay + wy = 288 + 10.598 = 298.598sx = ax + wx = 0 + 16.961 = 16.961convert the sum vector to polar form: s = sqrt( sx^2 + sy^2 ) = 299.079 mpht = arctan( sx / sy ) = 3.251 degreesanswer: the airplane will fly a bearing of (180 + 3.251) = 183.251 degrees at a ground speed of 299.079 mph