Olympiad Test: Algebraic Expressions - 1 - Free MCQ with solutions

(2xy – 3y² + 2x²) – (x² – xy + y²)
= 2xy – 3y² + 2x² – x² + xy – y²
= x² + 3xy – 4y²

[7 – 2x + 3y – (2x – y)] – (4x + 7y – 5)
= 7 – 2x + 3y – 2x + y – 4x – 7y + 5
Grouping the like terms:
(7 + 5) + (3y + y - 7y) + (-2x -2x -4x)
12 - 3y - 8x
Rearranging the terms:
= –8x – 3y + 12

Sum = (3x² + 5y²) + (x²– 4y²) = 4x² + y²
Difference = (2x² + 3y²) –(x² –y²)
= 2x² + 3y² –x² + y²
= x² + 4y²
Product = (4x² + y²) (x² + 4y²)
= 4x⁴ + 16x²y² + x²y² + 4y⁴
= 4x⁴ + 17x²y² + 4y⁴

(2.6 m²n) × (5 mn²)
= 2.6 × 5 × m²× m × n × n²

a(b – c) + b(c – a) + c(a – b)
= ab – ac + bc – ab + ac – bc = 0

a(b – c) –b(c – 2a) – c(2a – b)
= ab – ac – bc + 2ab – 2ac + bc
= 3ab – 3ac = 3(ab – ac)

(x³ + y³) (x²– y²)
= (x³) (x²) – (x³) (y²) + (y³) (x²) – (y³)(y²)
= x⁵ – x³y² + x²y³ – y⁵