Expansion of (x + a) (x +b)

Expansion of (x + a) (x +b)

          Which two quantities are to be multiplied ? (x +a) and (x + b). which is the equal term in (x + a) (x + b) ?      ……….. x.

          Which are the unequal terms in the quantities (x + a) and                        (x + b) ?                                       ……. a and b

          Study the following multiplication shown in horizontal arrangement.

(x + a) (x + b)       = x × (x + b) + a × (x + b)

                             = x² + xb + ax + ab

                             = x² + ax + bx + ab

                             = x² + (a + b)x + ab

Which are the terms in the product ?    ……x², (a+b)x and ab

What is the characteristic of the first term ?

………… square of the equal term.

What is the characteristic of the second term ?

…… Sum of the two unequal terms multiplied by the equal term.

What is the characteristic of the third term ?

……..product of the unequal terms.

This can be written in words as follows.

(equal term + first unequal term) (equal term + second unequal term)

= (equal term)² + (sum of unequal terms) × (equal term) + (product of unequal terms)

This gives us the following formula.

(x+a) (x+b) = x² + (a+b)x  + ab