The Algebraical principle involved is as follows:-
suppose we have to multiply (ax+b) by (cx+d).The product is
In other words, the first term, i.e;
the coefficient of x2 is got by vertically multiplication of a and c ; the middle
term , i.e; the coefficient of x is obtained by the cross-wise multiplication
of a and d and of b and c and the addition of the two products; and the
independent term is arrived at by the vertical multiplication of the absolute
terms . And as all arithmetical numbers are merely algebraic expressions in x,
the algebraic principle explained above is readily applicable to arithmetical
numbers too.
Formula for algebraic expression if our multiplicand and multiplier be of 2 digits :-
Formula:-
Example:-
Multiply (4x+7) by (3x+2)
Example:-
Multiply (4x+7) by (3x+2)
Now, if our multiplicand and multiplier be of 3 digit each, it merely means that we are multiplying
we observe here the following facts:
(i) the coefficient of x4 is got by the vertical multiplication of the first digit from the left side;
(iii) that the coefficient of x2 is obtained by the multiplication of the first digit of the multiplicand by the last digit of the multiplie, of the middle one by middle one and of the last one by the first one and by the addition of all the three products;
(iv) that the coefficient of x is obtained by the cross-wise multiplication of the second digit by the third one and conversely by the addition of the two products ; and(v) that the independent term results from the vertical multiplication of the last digit by the last digit.
Formula for 3 digit Algebraical Expression :-
Formula:-
Example:-
Multiply (3x2+2x+4) by (7x2+3x+7)
