ABSTRACT
Replacing p, q and r with their numerical values gives:
4p2qr3 = 4(2)2 (
1 2
)( 3 2
= 4× 2× 2× 1 2
× 3 2
× 3 2
× 3 2
= 27
Problem 3. Find the sum of: 3x , 2x , −x and −7x
The sum of the positive term is: 3x+2x=5x The sum of the negative terms is: x+7x=8x Taking the sum of the negative terms from the sum of the positive terms gives:
5x − 8x = −3x Alternatively
3x + 2x + (−x)+ (−7x) = 3x + 2x − x − 7x = −3x
Problem 4. Find the sum of: 4a, 3b, c, −2a, −5b and 6c
Each symbol must be dealt with individually. For the ‘a’ terms: +4a−2a=2a For the ‘b’ terms: +3b−5b=−2b For the ‘c’ terms: +c+6c=7c Thus
4a + 3b+ c+ (−2a)+ (−5b)+ 6c = 4a+ 3b+ c− 2a − 5b+ 6c = 2a− 2b+ 7c
Problem 5. Find the sum of: 5a−2b, 2a+c, 4b−5d and b−a+3d−4c
The as shown b’s, c’s and d’s. Thus:
+5a−2b +2a +c
+4b − 5d −a+ b − 4c+ 3d
Adding gives: 6a+ 3b− 3c− 2d
Problem 6. Subtract 2x+3y−4z from x−2y+5z
x −2y+5z 2x +3y−4z
Subtracting gives: −x−5y +9z
(Note that +5z−−4z=+5z+4z=9z) An alternative method of subtracting algebraic
expressions is to ‘change the signs of the bottom line and add’. Hence:
x−2y +5z −2x −3y +4z
Adding gives: −x −5y+9z
Problem 7. Multiply 2a+3b by a+b
Each term in the first expression is multiplied by a, then each term in the first expression is multiplied by b, and the two results are added. The usual layout is shown below.
