Subtract the second expression from the first expression(i) 2a + b, a

1.	Subtract the second expression from the first expression(i) 2a + b, a – b(ii) x + 2y + z , – x – y – 3z(iii) 3a2 – 8ab – 2b2, 3a2 – 4ab+6b2(iv) 4pq – 6p2 – 2q2, 9p2(v) 7 – 2x – 3x2, 2x2 – 5 x – 3(vi) 5x2 – 3xy – 7y2 , 3x2 – xy – 2y2(vii) 6m3 + 4m2 + 7m – 3 , 3m3 + 4
Answer» (i) 2a + b, a – b = 2a + b – a + b = (2a – a) + (b + b) = a + 2b ii) (x + 2y + z) – ( – x – y – 3z) = x + + z + x + y + 3z =(x + x) + (2y + y) +(z + 3z) = 2x + 3y + 4z iii) (3a² – 8ab – 2b²) – (3a² – 4ab + 6b²) = 3a² – 8ab – 2b² – 3a² +4ab – 6b² = (3a² – 3a²) + ( – 8ab + 4ab) + (2b² – 6b²) = 0 – 4ab – 8b² = – 4ab – 8b² iv) (4pq – 6p² – 2q²) – (9p²) = 4pq – 6p² – 2q² – 9p² = 4pq – 15p² – 2q² v) (7 – 2x – 3x²) – (2x² – 5x – 3) =7 – 2x – 3x² – 2x² + 5x + 3 = ( – 3x² – 2x²) + ( – 2x + 5x) + (7 + 3) = – 5x² + 3x + 10 vi) (5x² – 3xy – 7y²) – (3x² – xy – 2y²) = 5x²– 3xy – 7y² – 3x² + xy + 2y² = (5x² – 3x²) + ( – 3xy + xy) + ( – 7y² + 2y²) = 2x² – 2xy – 5y² viii) (6m³ + 4m² + 7m – 3) – (3m³ + 4) = 6m³ + 4m² + 7m – 3 – 3m3 – 4 = (6m³ – 3m³) + 4m² + 7m + (- 3 – 4) = 3m³ + 4m² + 7m – 7

Subtract the second expression from the first expression(i) 2a + b, a – b(ii) x + 2y + z , – x – y – 3z(iii) 3a2 – 8ab – 2b2, 3a2 – 4ab+6b2(iv) 4pq – 6p2 – 2q2, 9p2(v) 7 – 2x – 3x2, 2x2 – 5 x – 3(vi) 5x2 – 3xy – 7y2 , 3x2 – xy – 2y2(vii) 6m3 + 4m2 + 7m – 3 , 3m3 + 4

Answer»

(i) 2a + b, a – b

= 2a + b – a + b

= (2a – a) + (b + b)

= a + 2b

ii) (x + 2y + z) – ( – x – y – 3z)

= x + + z + x + y + 3z

=(x + x) + (2y + y) +(z + 3z)

= 2x + 3y + 4z

iii) (3a² – 8ab – 2b²) – (3a² – 4ab + 6b²)

= 3a² – 8ab – 2b² – 3a² +4ab – 6b²

= (3a² – 3a²) + ( – 8ab + 4ab) + (2b² – 6b²)

= 0 – 4ab – 8b²

= – 4ab – 8b²

iv) (4pq – 6p² – 2q²) – (9p²)

= 4pq – 6p² – 2q² – 9p²

= 4pq – 15p² – 2q²

v) (7 – 2x – 3x²) – (2x² – 5x – 3)

=7 – 2x – 3x² – 2x² + 5x + 3

= ( – 3x² – 2x²) + ( – 2x + 5x) + (7 + 3)

= – 5x² + 3x + 10

vi) (5x² – 3xy – 7y²) – (3x² – xy – 2y²)

= 5x²– 3xy – 7y² – 3x² + xy + 2y²

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

= 2x² – 2xy – 5y²

viii) (6m³ + 4m² + 7m – 3) – (3m³ + 4)

= 6m³ + 4m² + 7m – 3 – 3m3 – 4

= (6m³ – 3m³) + 4m² + 7m + (- 3 – 4)

= 3m³ + 4m² + 7m – 7