Page 12 - Algebra 1

Explanation
1. Let the number of balls with Bianca be x.
Number of balls with Greg = x + 20
Number of balls with Ron = x + x + 20 + 4 = 2x + 25
2. 3.9 can be written as (4 – 0.1)2
Use the identity, (a – b)2= a2 – 2ab + b2 (4–0.1)2 =42 –2×4×0.1+0.12
= 16 – 0.8 + 0.01 = 15.21
3. (x2+4)(x2 –4)+16
Usetheidentity,(a+b)(a–b)=a2 –b2
(x2)2 – 42 + 16
x4– 16 + 16 x4
4. Putx=1 in2x(6x–1), 2
11
2× (6× -1)
22
1 (3 – 1) 2
5. 2c(3c2 –5c+2)and4(c3 +3c2 –5c)
When adding two algebraic expressions, simplify and combine the like terms. 2c(3c2 –5c+2)=6c3 –10c2 +4c
4(c3 +3c2 –5c)=4c3 +12c2 –20c
The like terms are 6c3 and 4c3, – 10c2 and 12c2, 4c and –20c
Add the like terms
10c3 + 2c2 – 16c
6. Let the length of the plot of the sunflower be x meter. Length of the plot of the roses = (x + 5) meters
The area of the sunflower plot = x2 Theareaoftheroseplot=(x+5)2 =x2 +10x+25 Required expression = (x2 +10x + 25) – x2 = 10x + 25
7. 3m+4n–9–Expression=–5m+2n+8? Expression = 3m + 4n – 9 – (–5m + 2n + 8)
Expression = 3m + 4n – 9 + 5m – 2n – 8 Expression = 8m + 2n – 17
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ALGEBRA