The problem of combining similar items and removing brackets in mathematics of grade one in junior high school Given 2x & # 178; + xy = 10,3y & # 178; + 2XY = 6, find the value of 4x & # 178; + 8xy + 9y & # 178

The problem of combining similar items and removing brackets in mathematics of grade one in junior high school Given 2x & # 178; + xy = 10,3y & # 178; + 2XY = 6, find the value of 4x & # 178; + 8xy + 9y & # 178

Analysis: through observation, 8xy can be divided into 2XY + 6xy, and the common factor can be extracted from the remaining two combinations, and then the values of 2x & # 178; + XY, 3Y & # 178; + 2XY can be calculated as a whole
∵4x²+8xy+9y²=4x²+2xy+9y²+6xy=2（2x²+xy）+3（3y²+2xy）,
2x²+xy=10,3y²+2xy=6,
∴2（2x²+xy）+3（3y²+2xy）=2×10+3×6=38．
So the answer is: 38

On the problem of removing brackets of the same kind items in the first grade mathematics of junior high school
When k = (), the algebraic formula x6-5kx4 Y3 + 5 / 1x4 Y3 + 10 does not contain the term of X4 Y3

Because there is no fourth power term of X and the third power term of Y
So the fourth power of - 5K x, the third power of Y + the fourth power of 1 / 5 x, the third power of y = 0
So k = one in 25

Let's make some questions about merging similar items in the first grade of junior high school a little simpler,

3（5x-4)+45x=
7[3x(5+6)-7x]-10x=
12x+4x-5(2-4x)=
45[3x+4-5(x-2)]+90x=
Hope to help you

Exercises of merging similar items and mixed operation of rational numbers
Do not answer, as long as the number, preferably without braces
The merging of the same kind and the mixed operation are 105
I want what's in the book to be my own
Thank you
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Close the question before 3 p.m
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5xy + {xy - [xyz -3xz] } +3xy -5xzy
2(2y - 4) - (3x -3y) + x
6t + 3 - 6y + xy - 4t + 6y + t
3 (4n-m) - N + 3M, where n = - 2, M = 3

Combining similar items and rational number mixed operation exercises
105 each

Example 1. Merging similar items
（1）(3x-5y)-(6x+7y)+(9x-2y)
（2）2a-[3b-5a-(3a-5b)]
（3）(6m2n-5mn2)-6(m2n-mn2)
（1）(3x-5y)-(6x+7y)+(9x-2y)
=3x-5y-6x-7y + 9x-2y (remove brackets correctly)
=(3-6 + 9) x + (- 5-7-2) y (merge congeners)
=6x-14y
(2) 2A - [3b-5a - (3a-5b)]
=2A - [3b-5a-3a + 5B] (remove parentheses first)
=2A - [- 8A + 8b] (merge similar items in time)
=2A + 8a-8b (without brackets)
=10a-8b
(3) (6m2n-5mn2) - 6 (m2n-mn2) (note the factor 6 before the second bracket)
=6m2n-5mn2-2m2n + 3mn2
=(6-2) m2N + (- 5 + 3) Mn2
=4m2n-2mn2
Example 2: a = 3x2-4xy + 2Y2, B = x2 + 2xy-5y2
Find: (1) a + B (2) A-B (3) if 2a-b + C = 0, find C
(1）A+B=(3x2-4xy+2y2)+(x2+2xy-5y2)
=3x2-4xy + 2Y2 + x2 + 2xy-5y2 (without brackets)
=(3 + 1) x2 + (- 4 + 2) XY + (2-5) Y2 (merge congeners)
=4x2-2xy-3y2 (in descending order of x)
（2）A-B=(3x2-4xy+2y2)-(x2+2xy-5y2)
=3x2-4xy + 2y2-x2-2xy + 5y2 (without brackets)
=(3-1) x2 + (- 4-2) XY + (2 + 5) Y2 (merge congeners)
=2x2-6xy + 7y2 (in descending order of x)
（3）∵2A-B+C=0
∴C=-2A+B
=-2(3x2-4xy+2y2)+(x2+2xy-5y2)
=-6x2 + 8xy-4y2 + x2 + 2xy-5y2
=(- 6 + 1) x2 + (8 + 2) XY + (- 4-5) Y2 (merge congeners)
=-5x2 + 10xy-9y2 (in descending order of x)
Example 3. Calculation:
（1）m2+(-mn)-n2+(-m2)-(-0.5n2)
（2）2(4an+2-an)-3an+(an+1-2an+1)-(8an+2+3an)
(3) Simplification: (X-Y) 2 - (X-Y) 2 - [(X-Y) 2 - (X-Y) 2]
（1）m2+(-mn)-n2+(-m2)-(-0.5n2)
=M2-mn-n2-m2 + N2 (without brackets)
=(-) m2 Mn + (-) N2
=-M2-mn-n2 (in descending order of M)
（2）2(4an+2-an)-3an+(an+1-2an+1)-(8an+2+3an)
=8An + 2-2an-3an-an + 1-8an + 2-3an (without brackets)
=0 + (- 2-3-3) An-an + 1 (merge congeners)
=-an+1-8an
(3) (X-Y) 2 - (X-Y) 2 - [(X-Y) 2 - (X-Y) 2] [take (X-Y) 2 as a whole]
=(X-Y) 2 - (X-Y) 2 - (X-Y) 2 + (X-Y) 2 (remove brackets)
=(1 -- +) (X-Y) 2 ("merge congeners")
=(x-y)2
Example 4 find the value of 3x2-2 {X-5 [x-3 (x-2x2) - 3 (x2-2x)] - (x-1)}, where x = 2
Analysis: because the given formula is more complex, in general, we should simplify the integral first, and then substitute the given value x = - 2, pay attention to the sign when removing the brackets, and merge the similar terms in time to make the operation simple
The original formula = 3x2-2 {X-5 [x-3x + 6x2-3x2 + 6x] - x + 1} (without parentheses)
=3x2-2 {X-5 [3x2 + 4x] - x + 1} (merge similar items in time)
=3x2-2 {x-15x2-20x-x + 1} (without brackets)
=3x2-2 {- 15x2-20x + 1} (simplifying the formula in braces)
=3x2 + 30x2 + 40x-2 (without braces)
=33x2+40x-2
When x = - 2, the original formula is 33 × (- 2) 2 + 40 × (- 2) - 2 = 132-80-2 = 50
Example 5. If 16x3m-1y5 and - x5y2n + 1 are of the same kind, find the value of 3M + 2n
∵ 16x3m-1y5 and - x5y2n + 1 are similar terms
The times corresponding to X and y should be equal respectively
Ψ 3m-1 = 5 and 2n + 1 = 5
Ψ M = 2 and N = 2
∴3m+2n=6+4=10
This topic examines our understanding of the concept of similar terms
Example 6. Given x + y = 6, xy = - 4, find the value of (5x-4y-3xy) - (8x-y + 2XY)
(5x-4y-3xy)-(8x-y+2xy)
=5x-4y-3xy-8x+y-2xy
=-3x-3y-5xy
=-3(x+y)-5xy
∵x+y=6,xy=-4
The original formula = - 3 × 6-5 × (- 4) = - 18 + 20 = 2
Note: after the simplification of this problem, it is found that the result can be written in the form of - 3 (x + y) - 5xy, so the value of X + y, XY can be substituted into the original formula to get the final result, and there is no need to find out the value of X, Y. this thinking method is called overall substitution. I hope students can pay attention to it in the process of learning
3、 Practice
（1） Calculation:
（1）a-(a-3b+4c)+3(-c+2b)
（2）(3x2-2xy+7)-(-4x2+5xy+6)
（3）2x2-{-3x+6+[4x2-(2x2-3x+2)]}
（2） Simplification
（1）a>0,b

All negative integers with absolute values greater than 2.5 and less than 7.2 are______ ．

∵ if the absolute value is greater than 2.5 and less than 7.2, it can be set as X, ∵ if there are 2.5 ＜| x | 7.2, ∵ x | = 3, 4, 5, 6, 7, ∵ if the absolute value is greater than 2.5 and less than 7.2, all negative integers are: - 3, - 4, - 5, - 6, - 7; so the answer is: - 3, - 4, - 5, - 6, - 7;

On positive and negative numbers
① If there is a point a on the number axis, move point a to the right by 3 units to point B, and move point a to the left by 1 unit to point C, then calculate the distance between point B and point C; ② if the number represented by point a is - 1, calculate the number represented by point B and point C, [and express points a, B, and C on the number axis.] (needless to say this step.)

B=A+3
C=A-1
B-C=（A+3）-（A-1）=4
Similarly, a = - 1 can be obtained by substituting the above formula
B=2
C=-2

Who can please upload the absolute value of mathematics homework in volume one of grade seven?

1. Connect / - 3 /, - / - 4 /, 0 with ">" and "<", the correct is a. / - 3 / > - / - 4 / > 0, B. / - 3 / > 0 > - / - 4 / C. - / - 4 / < / - 3 / < 0, d.0 < - / - 4 / < / - 3 / 2. Given / X / = 3, / Y / = 2, x, y is different sign, then the value of X + y is equal to A.5 or - 5 B.1 or - 1 C.5 or 1 D. - 5 or - 13. A is

Find the sum of all positive integers with absolute value greater than 3 and less than 7.8

For self calculation, integers include positive integers and negative integers. Because it is the absolute value of positive integers, the answer is 4 + 5 + 6 + 7. Because it is greater than 3, 3 is not considered

Mathematics Grade 7 Volume 1 absolute value calculation
- 3 + 10 - 1
- 24 / - 3 x - 2
(5 / 6 - 1 / 2 + 1 / 3) x - 6

- 3 + 10 - 1
=3+10-1
=13-1
=12
2 - 3
=24÷3×2
=16
(5 / 6 - 1 / 2 + 1 / 3) x - 6
=(5/6-1/2+1/3)×6
=5/6×6-1/2×6+1/3×6
=5-3+2
=4