Question

Multiply:

(1) 4 (y² − 2y + 7)
(2) 6 (2a² − 3a − 5)
(3) 7x (3x² − 5x + 8)
(4) (m² − 4m + 6) 2m
(5) (4p² + p + 3) 9p
(6) 3a (a² + 4a − 6)
(7) 5q (2a + 3b − 4c)
(8) 4m (3mn − 2n² + 5)
(9) (x²y² + xy + 1) xy
(10) 11p²q (p² − 3pq + 8q²)

Answer 1

(1) 4 (y² − 2y + 7)
= (4 × y²) − (4 × 2y) + (4 × 7)
= 4y² − 8y + 28

(2) 6 (2a² − 3a − 5)
= (6 × 2a²) − (6 × 3a) − (6 × 5)
= 12a² − 18a − 30

(3) 7x (3x² − 5x + 8)
= (7x × 3x²) − (7x × 5x) + (7x × 8)
= 21x³ − 35x² + 56x

(4) (m² − 4m + 6) 2m
= (m² × 2m) − (4m × 2m) + (6 × 2m)
= 2m³ − 8m² + 12 m

(5) (4p² + p + 3) 9p
= (4p² × 9p) + (p × 9p) + (3 × 9p)
= 36p³ + 9p² + 27p

(6) 3a (a² + 4a − 6)
= (3a × a²) + (3a × 4a) − (3a × 6)
= 3a³ + 12a² − 18a

(7) 5q (2a + 3b − 4c)
= (5q × 2a) + (5q × 3b) − (5q × 4c)
= 10aq + 15bq − 20 qc

(8) 4m (3mn − 2n² + 5)
= (4m × 3mn) − (4m × 2n²) + (4m × 5)
= 12m²n − 8mn² + 20m

(9) (x²y² + xy + 1) xy
= (x²y² × xy) + (xy × xy) + (1 × xy)
= x³y³ + x²y² + xy

(10) 11p²q (p² − 3pq + 8q²)
= (11p²q × p²) − (11p²q × 3pq) + (11p²q × 8q²)
= 11p⁴q − 33p³q² + 88p²q³