Question

Add:

a) 9pq , -5pq , 3pq , -pq b) 3p-4q , 2p-3q c) 4x2 + 3y2 + 4xy , 5x2 + 8y2+12xy
d) 3pq + 4qr + 8r2

, 4pq + 6pr + 4p2
, 8pr + 2p2
e) 0.5x + 2y2 – 0.8xy , 0.8x2 + 4y2 + 0.8xy

f) 5a – 8b + 2c , -4b + 3c -2a , 6b – c – a
4) Subtract:
a) -6a + b + 3c + 8 from a – 2b – 5c – 8 b) 13xy – 6x2 + 4a2 – 1 from 25x2 + 16xy – 3a2 – 2
c) 4x – 12xy + 8y – 3 from 8x – 20xy + 10y + 4 d) 2x2 – 3x – 4y2 + 2 from 4x2 – 8x – 5y2 – 5
e) 4x2 y + 3xy – 4y2 x + 2 from 4x2 y + 5xy + 2y2 x – 3 f) 0.4x2 – 0.2x – 1 from 0.9x2 + 0.8x + 5
5) Subtract the sum of 3l – 4m – 7n2 and 2l + 3m – 4n2

from 6l + 3m + n2
6) Subtract 3x – 4y – 7z from the sum of x - 3y + 2z and - 4x + 9y - 11z
7) Find each of the following products:
a) 3xy, 5x,0 b) (-2x2
) , 7a2x
7
, 6a3x
5 c) 3, 15x, (-23x2 y) d) 6
5
ab, 12
6
bc, 5
6
abc

e) 1
2
xy, (3x – 6y) f) xz, (x + y) g) -4y , (2z -3x) h) 1.5x, (10x2y – 100xy2
)

i)(5x +3), (7x +2) j) (3x2 + y2

),( 2x2 + 3y2

) k) (3x – 5y), (x +y)

8) Simplify and evaluate:
a) 3y (2y – 7) -3 (y – 4) – 63 for y = 2
b) 3x (4x3 + 5y) – 7y (2x + y) for x = 2 and y = (-1)
c) (2x +5) (3x-2) + (x +2) (2x-3) for x= (-2)
d) (15a2 – 6a) (a-2) + a (3 + 7a) for a = 2
9) Using suitable identities find the following products:
a) ( 2a + 3 ) ( 2a + 3 ) b) ( 4x – y ) ( 4x – y ) c) ( pq + 2 ) ( pq – 2 ) d) ( 1x2
- 16 ) ( 1x2
- 16 )

e) ( a2 + bc ) ( a2 – bc ) f) ( 3x + 2 ) ( 3x + 2 ) g) ( 2x
5
+ 9 ) ( 2x
5
+ 9 ) h) ( 1
4
x
2 – 16) ( 1
4
x
2 – 16)

i) (x2 +
2
x
) (x2
-
2
x
) j) (
x
4
-
2
x
) (
x
4
+
2
x
) k) ( 1.02 )2 – ( 0.98 )2

l) 194 × 206

m) ( 199 )2
n ) 178 × 178 – 22 × 22 o) (502)2

p) 9.3 × 8.7
10) Evaluate the following using the identity ( x + a ) ( x + b ) = x2 + ( a + b ) x + ab
a) (x + 7 ) ( x + 5 ) b) ( 3x – 7 ) ( 3x + 4 )
c) ( a + 1 ) ( a – 2 ) d) 52 × 47
e) 7.5 × 6.8 f) 98 × 97

11) Show that :
a) ( 3a + b) 2

_ ( 3a – b)2 = 12ab b) (x + 5) (2x – 1) = 2x2 + 9x – 5

c) (9a – 5b)2 + 180ab = (9a + 5b)2

d) (2x + 3y )2

- (2x - 3y)2 = 24 xy

12) Simplify:
a) (y- 5) (y+5) (y2 + 25) b) ( m2 – n

2 m)2+ 2m2 n
2
c) 2y (3y – 5) (2y +1)

d) ( 7m – 8n)2 + (7m + 8n)2

e)(2x -3x +5) (5x +2) f) (5-x)(6-5x)(2x-3)

Answer 1

Explanation:

Addition:

a) 9pq - 5pq + 3pq - pq = 6pq

b) 3p - 4q + 2p - 3q = 5p - 7q

c) 4x² + 3y² + 4xy + 5x² + 8y² + 12xy = 9x² + 11y² + 16xy

d) 3pq + 4qr + 8r² + 4pq + 6pr + 4p² + 8pr + 2p²

= 7pq + 4qr + 8r² + 14pr + 6p²

= 7p(q + 2r) + 2(2qr + 4r² + 3p²)

e) .5x + 2y² - .8xy + .8x² + 4y² + .8xy

= .5x + 6y² + .8x²

= x(.5 + .8x) + 6y²

f) 5a - 8b + 2c -4b + 3c - 2a + 6b - c - a

= 2a - 6b + 4c

= 2(a - 3b + 2c)

Subtraction:

term which comes after from will come as the first term for subtraction:

a) a - 2b - 5c - 8 - (-6a + b + 3c + 8)

= a - 2b - 5c - 8 + 6a - b - 3c - 8

= 7a - 3b - 8c - 16

= 7a - 3b - 8(c + 2)

b) 25x² + 16xy - 3a² - 2 - (13xy - 6x² + 4a² - 1)

= 25x² + 16xy - 3a² - 2 - 13xy + 6x² - 4a² + 1

= 31x² + 3xy - 7a² - 1

c) 8x - 20xy + 10y + 4 - (4x - 12xy + 8y - 3)

= 8x - 20xy + 10y + 4 - 4x + 12xy - 8y + 3

= 4x - 8xy + 2y + 7

= 4x(1 - 2y) + 2y + 7

d) 4x² - 8x - 5y² - 5 - (2x² - 3x - 4y² + 2)

= 4x² - 8x - 5y² - 5 - 2x² + 3x + 4y² - 2

= 2x² - 5x - y² - 7

e)4x²y + 5xy + 2y²x - 3 - (4x²y + 3xy - 4y²x + 2)

= 4x²y + 5xy + 2y²x - 3 - 4x²y - 3xy + 4y²x - 2

= 2xy + 6y²x - 5

= 2xy(1 + 3y) - 5

f) .9x² + .8x + 5 - (.4x² - .2x - 1)

= .9x² + .8x + 5 - .4x² + .2x + 1

= .5x² + x + 6

Addition than Subtraction:

sum = 3l - 4m - 7n² + 2l + 3m - 4n²

= 5l - m - 11n²

subtraction = 6l + 3m + n² - (5l - m - 11n²)

= 6l + 3m + n² - 5l + m + 11n²

= l + 4m + 12n²

= l + 4(m + 3n²)

Addition than Subtraction:

sum = x - 3y + 2z - 4x + 9y - 11z

= -3x + 6y - 9z

subtraction = -3x + 6y - 9z - (3x - 4y - 7z)

= -3x + 6y - 9z - 3x + 4y + 7z

= -6x + 10y - 2z

= 2(-3x + 5y - z)

Products:

a) 3xy * 5x * 0 = 0

b) -2x² * 7a²x * 6a³x * 7 * 5 = -2940x⁴a⁵

c) 3 * 15x * -23x²y = -1035x³y

d) 6 * 5 * ab * 12 * 6 * bc * 5 * 6 * abc

= 64800a²b³c²

e) 12xy(3x - 6y) = 36x²y - 72xy²

f) xz(x + y) = x²z + xyz

g) -4y(2z - 3x) = -8yz + 12xy

h) 1.5x(10x²y - 100xy²) = 15x³y - 150x²y²

i) (5x + 3)(7x + 2)

= 35x² + 10x + 21x + 6

= 35x² + 31x + 6

j) (3x² + y²)(2x² + 3y²)

= 6x⁴ + 9x²y² + 2x²y² + 3y⁴

= 6x⁴ + 11x²y² + 3y⁴

k) (3x - 5y)(x + y)

= 3x² + 3xy - 5xy - 5y²

= 3x² - 2xy - 5y²