S1 maths Addition and Subt....

1.
(x + 2) + (8x - 3) + (30 - 2x)
= x + 2 + 8x - 3 + 30 - 2x
= (x + 8x - 2x) + (2 - 3 + 30)
= 7x + 29


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2.
(1 - y) - (2y + 3) + (3y - 5)
= 1 - y - 2y - 3 + 3y - 5
= (-y - 2y + 3y) + (1 - 3 - 5)
= -7


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3.
(x + y) + (y - z) - (x - z)
= x + y + y - z - x + z
= (x - x) + (y + y) + (-z + z)
= 2y


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4.
(3a + b) - (2b - c) + (3c - 2a)
= 3a + b - 2b + c + 3c - 2a
= (3a - 2a) + (b - 2b) + (c + 3c)
= a - b + 4c


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5.
(s² - t + 2) - (3s² - 3t + st)
= s² - t + 2 - 3s² + 3t - st
= (s² - 3s²) + (-t + 3t) +2 - st
= -2s² + 2t + 2 - st


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6.
(4r² + 5s²) + (7r² - 3s² + 6rs)
= 4r² + 5s² + 7r² - 3s² + 6rs
= (4r² + 7r²) + (5s² - 3s²) + 6rs
= 11r²+ 2s² + 6rs


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7.
(2m² - 3n² - mn) - (5m² - n²)
= 2m² - 3n² - mn - 5m² + n²
= (2m² - 5m²) + (-3n² + n²) - mn
= -3m² - 2n² - mn


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8.
(8x³ + 4x - 5x²) - (5x² + x + 9x³)
= 8x³ + 4x - 5x² - 5x² - x - 9x³
= (4x - x) + (-5x² - 5x²) + (8x³ - 9x³)
= 3x - 10x² - x³


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9.
(y² - 1) + (-y + y²) - (2 - y + y²)
= y² - 1 + -y + y² - 2 + y - y²
= (-1 - 2) + (-y + y) + (y² + y² - y²)
= -3 + y²


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10(a)
(1 - a - 2a²) + (a³ + 2a² - a)
= 1 - a - 2a² + a³ + 2a² - a
= a³ + (-2a² + 2a²) + (-a - a) + 1
= a³ - 2a + 1

10
(b)
When a = -2, expression
= a³ - 2a + 1
= (-2)³ - 2(-2) + 1
= -3


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11.
When x = 3 and y = 4, the total amount
= $[(x + 6y) + (8y - x)]
= $[x + 6y + 8y - x]
= $[(x - x) + (6y + 8y)]
= $14y
= $14(4)
= $56

首先要記住：正正得正 (+ + = +)正負得負 (+ - = -)負正得負 (- + = -)負負得正 (- - = +)即係如果括號前面係＋括號入面個符號唔使轉eg. +(x+y) = +x+y +(x-y) = +x-y +2(x+y) = +2x+2y 2(x+y) = 2x+2y
+2(x-y) = +2x-2y
2(x-y) = 2x-2y
但係如果括號前面符號係－括號入面個符號就要轉eg. -(x+y) = -x-y -(x-y) = -x+y -2(x+y) = -2x-2y -2(x-y) = -2x+y

Simplify the following expressions.Please give me the solutions and the answers,thanks!

1. (x+2)+(8x-3)+(30-2x)= x+2+8x-3+30-2x= x+8x-2x+2-3+30= 7x+29

2. (1-y)-(2y+3)+(3y-5)= 1-y-2y-3+3y-5= -y-2y+3y+1-3-5= -7
3. (x+y)+(y-z)-(x-z)= x+y+y-z-x+z= x-x+y+y-z+z= 2y
4. (3a+b)-(2b-c)+(3c-2a)= 3a+b-2b+c+3c-2a= 3a-2a+b-2b+c+3c= a-b+4c

5. (s²-t+2)-(3s²-3t+st)= s²-t+2-3s²+3t-st
= s²-3s²-t+3t-st+2
= -2s²+2t-st+2

6. (4r²+5s²)+(7r²-3s²+6rs)
= 4r²+5s²+7r²-3s²+6rs
= 4r²+7r²+5s²-3s²+6rs
= 11r²+2s²+6rs

7. (2m²-3n²-mn)-(5m²-n²)
= 2m²-3n²-mn-5m²+n²
= 2m²-5m²-3n²+n²-mn
= -3m²-2n²-mn

Simplify the following expressions and arrange the terms in ascending powers of the variables.

8. (8x³+4x-5x²)-(5x²+x+9x³)
= 8x³+4x-5x²-5x²-x-9x³
= 4x-x-5x²-5x²+8x³-9x³
= 3x-10x²-x³

9. (y²-1)+(-y+y²)-(2-y+y²)
= y²-1-y+y²-2+y-y²
= -1-2-y+y+y²+y²-y²
= -3+y²

10a. (1-a-2a²)+(a³+2a²-a)
= 1-a-2a²+a³+2a²-a
= a³-2a²+2a²-a-a+1
= a³-2a+1

10b. When a = -2,
(1-a-2a²)+(a³+2a²-a)
= a³-2a+1
= (-2)³-2(-2)+1
= -8+4+1
= -3

11. Mary has $(x+6y), Tim has $(8y-x).
When x=3 and y=4,
The total amount they have
= $(x+6y)+$(8y-x)
= $(x+6y+8y-x)
= $(14y)
= $(14 x 4)
= $56

Both lop and micatkie are helpful.

However, lop has made mistakes in Q.(2) and Q.(10)b.

lop is very helpful.