4a2 + 3b2 +6b + 3 subtract this from 6a2 - 4ab + 8b2 +3a ko
Answers
Step-by-step explanation:
To refresh understanding of conventions in algebra as applied to addition and subtraction
[LO 1.2, 1.6]
A We will first have a look at terms.
Remember, terms are separated by + or –. In each of the following, say how many terms there are:
1. a + 5
2. 2a2
3. 5a (a+1)
4. 3a−1a2+5a size 12{ { {3 size 11{a} - 1} over { size 11{a rSup { size 8{2} } }} } size 12{+5a}} {}
In the next exercise you must collect like terms to simplify the expression:
1. 5a + 2a
2. 2a2 + 3a – a2
3. 3x – 6 + x + 11
4. 2a(a–1) – 2a2
B Adding expressions
Example:
Add 3x + 4 by x + 5.
(x + 5) + (3x + 4) Write, with brackets, as sum.
x + 5 + 3x + 4 Remove brackets, with care.
4x + 9 Collect like terms.
In this exercise, add the two given expressions:
1. 7a + 3 and a + 2
2. 5x – 2 and 6 – 3x
3. x + ½ and 4x – 3½
4. a2 + 2a + 6 and a – 3 + a2
5. 4a2 – a – 3 and 1 + 3a – 5a2
C Subtracting expressions
Study the following examples very carefully:
Subtract 3x – 5 from 7x + 2.
(7x + 2) – (3x – 5)
Notice that 3x – 5 comes second, after the minus.
7x + 2 – 3x + 5
The minus in front of the bracket makes a difference!
4x + 7
Collecting like terms.
Calculate 5a – 1 minus 7a + 12: (5a – 1) – (7a + 12)
5a – 1 – 7a – 12
–2a – 13
D Mixed problems
Do the following exercise (remember to simplify your answer as far as possible):
1. Add 2a – 1 to 5a + 2.
2. Find the sum of 6x + 5 and 2 – 3x.
3. What is 3a – 2a2 plus a2 – 6a?
4. (x2 + x) + (x + x2) = . . .
5. Calculate (3a – 5) – (a – 2).
6. Subtract 12a + 2 from 1 + 7a.
7. How much is 4x2 + 4x less than 6x2 – 13x?
8. How much is 4x2 + 4x more than 6x2 – 13x?
9. What is the difference between 8x + 3 and 2x +1?
Use appropriate techniques to simplify the following expressions:
1. x2 + 5x2 – 3x + 7x – 2 + 8
2. 7a2 – 12a + 2a2 – 5 + a – 3
3. (a2 – 4) + (5a + 3) + (7a2 + 4a)
4. (2x – x2) – (4x2 – 12) – (3x – 5)
5. (x2 + 5x2 – 3x) + (7x – 2 + 8)
6. 7a2 – (12a + 2a2 – 5) + a – 3
7. (a2 – 4) + 5a + 3 + (7a2 + 4a)
8. (2x – x2) – 4x2 – 12 – (3x – 5)
9. x2 + 5x2 – 3x + (7x – 2 + 8)
10. 7a2 – 12a + 2a2 – (5 + a – 3)
11. a2 – 4 + 5a + 3 + 7a2 + 4a
12. (2x – x2) – [(4x2 – 12) – (3x – 5)]