Question

Use the identity (x + a) (x + b) = x² + (a + b)x + ab to find the following products.

(i) (x + 3) (x + 7) (ii) (4x +5) (4x + 1)

(iii) (4x − 5) (4x − 1) (iv) (4x + 5) (4x − 1)

(v) (2x +5y) (2x + 3y) (vi) (2a² +9) (2a² + 5)

(vii) (xyz − 4) (xyz − 2)

Answer 1

The products will be as follows.

(i) (x + 3) (x + 7) = x² + (3 + 7) x + (3) (7)

= x² + 10x + 21

(ii) (4x + 5) (4x + 1) = (4x)² + (5 + 1) (4x) + (5) (1)

= 16x² + 24x + 5

(iii)

= 16x² − 24x + 5

(iv)

= 16x² + 16x − 5

(v) (2x +5y) (2x + 3y) = (2x)² + (5y + 3y) (2x) + (5y) (3y)

= 4x² + 16xy + 15y²

(vi) (2a² +9) (2a² + 5) = (2a²)² + (9 + 5) (2a²) + (9) (5)

= 4a⁴ + 28a² + 45

(vii) (xyz − 4) (xyz − 2)

=

= x²y²z² − 6xyz + 8