Olympiad Test: Algebraic Expressions - 2 - Class 7 MCQ

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

Sum = –5x² + 7xy + 2y² + x² – 3xy – y²
= – 4x² + 4xy + y²
= –7 –(– 4x² + 4xy + y²)
= –7 + 4x²– 4xy – y²)

(0.8m – 0.7n) (1.5n – 1.7m)
= (0.8m)(1.5n) + (0.7n) (1.7m) – (0.7n)(1.5n) – (0.8m) (1.7m)
= 1.2mn + 1.19mn –1.05n² –1.36m²
= 2.39mn – 1.05n² – 1.36m²

0.3x² – 3xy + 0.8y² + 4x² – 2y² + 0.7xy
= (4 + 0.3) x² + (0.7 – 3) xy + (0.8 – 2)y²
= 4.3x² – 2.3xy –1.2y²

(7x⁴– x + 11) (x²– 3)
= 7x⁴ – 21x²– x³ + 3x + 11x² – 33
= 7x⁴– x³ – 10x² + 3x – 33

1.5a(10a²b –100ab²)
= 15a³b – 150a²b²

7x² – [x²– 3x –{x + y}] – (5x – 3y + 3)
= 7x² – x² – 3x – x + y – 5x + 3y – 3
= 6x² – x + 4y – 3

x(x + 4) + 3x (2x²– 3) +4x² + 5
= x 2 + 4x + 6x³– 9x + 4x² + 5
= 6x³ + 5x²– 5x + 5

4mn(m – n) – 6m²(n – n²) –3n²(2m² – m)
= 4 m²n – 4m – n² – 6m²n + 6m² n² – 6n²m² + 3n²m
= –2m²n – n²m = –mn(2m + n)

a²b(a – b²) –ab²(3ab – a²) – a³b (1 – 2b)
= a³b – a²b³ – 3a²b³ + a³b² – a³b + 2a³b²
= 3a³b²– 4a²b³