Algebra Quiz #1

Question 1

Simplify

(a)

(b)        2x⁴y² + 8xy² – 4x³y

Solutions:

(a)

(b)

2x⁴y² + 8xy² – 4x³y

Note: Only like terms can be added and or subtracted, there are no like terms in the Algebraic expression above.

Question 2

(a) Given m = 4, n = -3

Calculate,  (3m + n) (2m – 2)

(b)        x^*y = 4x – 3y

Find    6^*4

Solutions:

(a)

(3m + n) (2m – 2)

= (3 (4) + (-3) )   (2 (4) – 2)

= (12 – 3)  (8 – 2)

= (9)  (6)

= 54

(b)

       6^*4       =          4x – 3y

=          4(6) – 3(4)

=          24 – 12

=          12

Question 3

Factorize Completely

(a) 16p + 2q

(b)  169a² – 13a

Solutions:

(a)

16p + 2q =       2(8p + q)

(b)

169a² – 13a =  13a(13a – 1)

Question 4

Simplify:

(a)        (5³)²

(b)        b^1/4

Solutions:

(a)

(5³)²          =          5 ^{3 x 2}

=          5 ⁶

(b)

Question 5

Solve the Simultaneous equations:

5y + 6x = 28

2y + 3x = 13

Solution:

5y + 6x = 28 ——> Eq. 1

2y + 3x = 13 ——> Eq. 2

Multiply Eq. 2 by 2.

2(2y + 3x = 13)

4y + 6x = 26 ——> New Eq. 2

Eq.1 – New Eq.2

5y – 4y + 6x – 6x = 28 – 26

y = 2

Substitute 2 for y in Eq.1

5y + 6x = 28

5(2) + 6x = 28

10 + 6x = 28

6x = 28 – 10

6x = 18

x = 3

That is, x = 3 and y = 2