Expand and Simplify (x + 3) (x + 5)

by

(i) (x + 3) (x + 5)

(ii) (x + 3) (x – 5)

(iii) (x – 7) (x + 9)

(iv) (x – 2y) (x – 3y)

Answer :

(i) (x + 3) (x + 5)

By further calculation

= x2 + (3 + 5) x + 3 × 5

So we get

= x2 + 8x + 15

(ii) (x + 3) (x – 5)

By further calculation

= x2 + (3 – 5)x – 3 × 5

So we get

= x2 – 2x – 15

(iii) (x – 7) (x + 9)

By further calculation

= x2 – (7 – 9)x – 7 × 9

So we get

= x2 + 2x – 63

(iv) (x – 2y) (x – 3y)

By further calculation

= x2 – (2y + 3y)x + 2y × 3y

So we get

= x2 – 5xy + 6y2

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