Which of the equations are true identities? A. N ( n − 2 ) ( n + 2 ) = n 3 − 4 n B. ( x + 1 ) 2 − 2 x + y 2 = x 2 + y 2 + 1

Skip to content# Which of the equations are true identities? A. N ( n − 2 ) ( n + 2 ) = n 3 − 4 n B. ( x + 1 ) 2 − 2 x + y 2 = x 2 + y 2 + 1

Which of the equations are true identities? A. N ( n − 2 ) ( n + 2 ) = n 3 − 4 n B. ( x + 1 ) 2 − 2 x + y 2 = x 2 + y 2 + 1

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Comments (5) on “Which of the equations are true identities? A. N ( n − 2 ) ( n + 2 ) = n 3 − 4 n B. ( x + 1 ) 2 − 2 x + y 2 = x 2 + y 2 + 1”

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whatvare the choices

step-by-step explanation:

Here is the answer

communative

Both A and B are true identities

Step-by-step explanation:

A. N ( n − 2 ) ( n + 2 ) = n 3 − 4 n

We need to show that (left-hand-side)L.H.S = R.H.S (right-hand-side)

So,

n ( n − 2 ) ( n + 2 ) = n(n² - 2²) (difference of two squares)

= n³ - 2²n (expanding the brackets)

= n³ - 4n (simplifying)

So, L.H.S = R.H.S

B. ( x + 1 )² − 2x + y² = x² + y² + 1

We need to show that (left-hand-side)L.H.S = R.H.S (right-hand-side)

So,

( x + 1 )² − 2x + y² = x² + 2x + 1 - 2x + y² (expanding the brackets)

= x² + 2x - 2x + 1 + y² (collecting like terms)

= x² + 1 + y²

= x² + y² + 1 (re-arranging)

So, L.H.S = R.H.S

So, both A and B are true identities since we have been able to show that L.H.S = R.H.S in both situations.

idk

step-by-step explanation:

RATIONAL NUMBERS,ALGEBRAIC EXPRESSIONS,FACTORISATION,LINEAR EQUATIONS,SQUARES AND SQUARE ROOTS,CUBES AND CUBE ROOTS,EXPONENTS

1.Name the property of multiplication of the following rational numbers

-5/16 x 8/15 = 8/15 x -5/16

Associative

Transitive

Closure

Commutative

2. Ascending order for the following numbers is :

(-7)/5,(-7)/4,-1,(-7)/8,1

(-7)/5,(-7)/4,-1,(-7)/8,1

(-7)/4,(-7)/5,-1,(-7)/8,1

-1,(-7)/4,(-7)/5,,(-7)/8,1

None

3. Reciprocal of ((–3)/8×(-7)/13) is:

104/-21

39/56

104/21

d.-39/56

4. If x/2+1/3=1, then x =

¾

4/3

-3/4

d.-4/3

5.(-7)/13-(-(-8)/15)=

-239/195

29/195

-29/195

None

6.(-2)÷((-5)/3)=

5/6

-5/6

6/5

-6/5

7. 5/4-7/6-(-2)/3=

¾

-3/4

-7/12

7/12

8.Product of (3 1/7×1 5/6×1 2/5×1 1/11)

5 8/5

5 4/5

8 4/5

7 4/5

9.If (–5)/7=x/28.Find x.

10.Simplify :

(13/9×(-15)/2)+(7/3×8/5)+(3/5×1/2)

11. Find the value of (a+b)/(a-b) if a= 4/5 b = 7/9

12Find the area of a rectangular park which is m long and m broad.

13.Verify the property and name it

ALGEBRAIC EXPRESSIONS

1.Add

2.Add

3.Subtract

4.Subtract

5.Multiply

6.Multiply

7.Simplify:i)

ii)

8.Using suitable identities evaluate the following

9.Simplify (5x-7)(2x+3)(7x-8)

10.Divide 6x^3-x+19x^2 by x+3

FACTORISATION

Factorise the following

(i) (ii)

Linear Equations

II.Solve the following

Solve

SQUARES AND SQUARE ROOTS

1. Square root of 0.0016 is:

0.8

0.04

0.4

d. 0.08

2. Which of the following cannot be perfect squares?

841

529

198

d.All of the above

3. The hypotenuse of a right triangle with legs 3x and 4x will be

5x

7x

16x

d. 25x

4. Given that √4096=64,then find √(40.96)+√(0.4096)

74

60.4

64.4

d. 7.04

5.Find the square root of

25/13

26/13

27/13

d. 28/13

II.SOLVE THE FOLLOWING

1.Find the smallest number by which must be subtracted from 2361 to make it a perfect square.

2.Evaluate the square root of correct to three decimal places

3.Give two Pythagorean triplets with one member 5.

4.Find the square root of the rational number 625/6889.

5. 3600 soldiers are asked to stand in different rows. Every row has as many soldiers as there are rows.find the number of row

6.Find the perimeter of the square whose area is 6889 sqm.

CUBES & CUBEROOTS

√(3&0.000027×0.008)

0.6

0.0006

0.006

0.06

2. The cube root of .000343 is

0.7

0.07

0.007

d. 7

3. Which of the following is the cube root of -64/343?

7/4

-7/4

4/7

-4/7

4.

2

-5

3

-4

5. State true or false:

a. Cubes of a Prime Number are prime.

b. Cubes of all even natural numbers are even.

c. Cubes of all negative integers are positive integers

6. Find the number whose cube is 27000.

7.What is the smallest number by which 1323 may be multiplied so that the product is a perfect cube?

8.Show that √(3&27) x √(3&125)=√(3&27x125)

9.Find the value of √(3&968) x √(3&1375)

EXPONENTS

1. 3 × 102 + 2 × 101 + 9 × 100 + 2 × 10–1 + 5 × 10–2

a. 3292.5

b. 32.925

c. 0.32925

d. 329.25

2. Which of the following is the standard form of 0.00001275?

a.1.275 * 10-5

b.1.275 * 105

c.127.5 * 10-7

d.127.5 * 107

3. What is the reciprocal of (-3 / 4)0?

a. -1

b. 1

c. -4/3

d. 4/3

4. x/y= 3/2 then (x^2-y^2)/(x^2+y^2 ) =

a. 5/3

b. 5/13

c. 1/9

d. 13/5

5.If 2x.210 = 2-4x then value of x will be

a. -2

b. 4

c. 3

d. -1

II.

1. Simplify {(2/3)^2 }^3×(1/3)^(-4)×3^(-1)×6^(-1).

2. Find x so that (–5)x+1 × (–5)5 = (–5)7

3. Find the value of m so that (2/9)^3×(2/9)^(-6)=(2/9)^(2m-1)

4.Express in power notation

16/81

5.Find the value of

(-2)^5 divided by (-1/3)^4

6.Evaluate b^2 -9 (b-1)^2 if b=1.1[hint:put b= 11/10]

7.By what number should (-3/2)^-3 be multiplied,so that the product is (9/8)^-2