Question

Can’t you find these products on your own?

(i) (p + q) (2m + 3n)

(ii) (4x + 3y) (2a + 3b)

(iii) (4a + 2b) (5c + 3d)

(iv) (m + n) (5a + b)

(v) (2x + 3y) (x + 2y)

(vi) (3a + 2b) (x + 2y)

Answer 1

By the general principle, we know that:

(x + y) (u + v) = xu + xv + yu + yv

(i)

(p + q) (2m + 3n) = (p × 2m) + (p × 3n) + (q × 2m) + (q × 3n)

= 2pm + 3pn + 2qm + 3qn

(ii)

(4x + 3y) (2a + 3b) = (4x × 2a) + (4x × 3b) + (3y × 2a) + (3y × 3b)

= 8ax + 12bx + 6ay + 9by

(iii)

(4a + 2b) (5c + 3d) = (4a × 5c) + (4a × 3d) + (2b × 5c) + (2b × 3d)

= 20ac + 12ad + 10bc + 6bd

(iv)

(m + n) (5a + b) = (m × 5a) + (m × b) + (n × 5a) + (n × b)

= 5am + bm + 5an + bn

(v)

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

= 2x² + 4xy + 3xy + 6y²

(vi)

(3a + 2b) (x + 2y) = (3a × x) + (3a × 2y) + (2b × x) + (2b × 2y)

= 3ax + 6ay + 2bx + 4by