Chapter 5.4, Problem 1CE

To determine

To find:A BASIC program that produces the product $(Ax+B)(Cx+D)$ and to use its output to check the product $(x+3)(x+5)$ manually.

Explanation of Solution

Given information: A product of two factors $(Ax+B)(Cx+D)$ and another expression

  $(x+3)(x+5)$ , so that the out of first expression to be find by usinga

BASIC program.

Concept used:To get the product, multiply second factor by each term of first factor and then use distributive rule to expand it and add like terms together. Use PRINT command to print a statement and INPUT command to enter a variable`s value.

BASIC program to get product $(Ax+B)(Cx+D)$ is:

10 PRINT “Program to find product (Ax+B)(Cx+D)”;

20 PRINT “Enter values of A , B , C and D=“;

30 INPUT A,B,C,D;

40 (A*x+B)*(C*x+D)=(A*C)*x*x+(A*D+B*C)*x+B*D;

50 PRINT “(Ax+B)(Cx+D)=”;(A*C);”x^2+”;(A*D+B*C);”x+”;B*D; 60 END;

Output: Program to find product $(Ax+B)(Cx+D)$ .

Enter values of A,B,C,D=1 3 1 5

  $(Ax+B)(Cx+D)=x^2+8x+15$

Here line 10-20, print different messages. Line 30 asks for values of variables A , B , C and D to input. Line 40 simplifies the product of two factors given. LINE 50 returns the result of the given product.

Further simplify the given product as follows.

$(x+3)(x+5)=x(x+5)+3(x+5)$ ; FOIL rule

$=x^2+5x+3x+15$ ; Distributive rule $a(b+c)=ab+ac$

  $=x^2+8x+15$ ; Combining like terms

Conclusion: Above result calculated manually is correct as it is same as produced by the output of this BASIC program.