# Use the identity (x + a) (x + b) = x^2 + (a + b)x + ab to find the following products. (i) (x + 3) (x + 7) (ii) (4x +5) (4x + 1)

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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)

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(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) (4x - 5) (4x - 1)

= (4x)2 + [ (-5) + (-1) ] (4x) + (5) (-1)

= 16x2 + 16x -5

(iv) (4x + 5) (4x - 1)

= (4x)2 + [ (5) + (-1) ] (4x) + (5) (-1)

=16x2 + 16x − 5

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