Solve simultaneous linear equations: (i) 21×2 – 59xy + 40y2

Solve simultaneous linear equations:

(i) 21x² – 59xy + 40y²
(ii) 4x³y – 44x²y + 112xy

Solution:

(i) 21x² – 59xy + 40y²
By multiplying the first and last term we get, 21 × 40 = 840
Then, (-35) × (-24) = 840
So, 21x² – 35xy – 24xy + 40y²
7x(3x – 5y) – 8y(3x – 5y)
(3x – 5y) (7x – 8y)
(ii) 4x³y – 44x²y + 112xy
4x³y – 44x²y + 112xy
Take out common in all terms,
4xy(x² – 11x + 28)
Then, 4xy (x² – 7x – 4x + 28)
4xy [x(x – 7) – 4(x + 7)]
4xy (x – 7) (x – 4)

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