Expand or factor each of the following expressions to determine which expressions are equivalent.
(3x – 4y)²
912 + 31 - 20
(41 – 3y)²
(3x – 2) (9x2 + 6x + 4)
(3x + 5)(3x – 4)
(31 + 2) (912 - 61 + 4)
9.12 - 2414 + 1672
2713 - 8

1. 9x^2-24xy16y^2

2.

3.9y^2-246y+1681

4. 18x^2+54x-44

Step-by-step explanation:

1. (3x)^2-2*3x*4y+(4y)^2

9x^2-2*3x4y+(4y)^2

9x^2-24xy+(4y)^2

9x^2-24xy+16y^2

Ans: 9x^2-24xy+16y^2   the (*) are times

2. 912+31-20=923

ANS: 13*71

3. 1681-246y+9y^2

9y^2-246y+1681

ANS : 9y^2-246y+1681

4. 3x*(9*2+6x+4)-2(9*2+6x+4)

54x+18^2+12x-2(9*2+6x+4)

54x+18x^2+12x-36-12x-8

54x+18^2+12x-36-12x-8

54x+18x^2-36-8

18x^2+54x-36-8

18x^2+54x-44

Ans: 18x^2+54x-44

5. 3x*3x-3x*4+5*3x-5*4

9x^2-3x*4+5*3x-5*4

9x^2-12x+5*3x-5*4

9x^2-12x+15x-5*4

9x^2-12x+15x-20

ANS: 9x^2+3x-20

6. (31+2)(912-61+4)=28215

ANS : 3^3*5*11*19

7. 9.12-2414+1672

912/100-2414+1672

2^4*3*19/2^2*5^2 -2414+1672

2^4-2*3*19/5^2 -2414+1672

2^2*3*19/5^2 -742

(2^2*3*19)-5^2)742/5^2

(4*3*19)-25*742/5^2

228-18550/5^2

18322/5^2

8. 2713-8

2705

ANS: 5*541

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: