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
