The document provides solutions to problems involving multiplying polynomial expressions. It works through 33 examples of multiplying terms with variables like x, y, a. For each problem, it shows the step-by-step work and simplification to obtain the final product term as a monomial. It also verifies select solutions by plugging in values for the variables. The document uses these examples to demonstrate how to multiply polynomials and verify the solutions.

1. Find each of the following products (1-8)
Question 1.
5x2
x 4x3
Solution:
5x2
x 4x3
= 5 x 4 x x2
x x3
= 20x2 + 3
= 20xs
Question 2.
3a2
x 4b4
Solution:
-3a2
x 4b4
= -3 x 4 x a2
b4
= -12a2
b4
Question 3.
(-5xy) x (-3x2
yz)
Solution:
(-5xy) x (-3x2
yz)
= (-5) x (-3)xy x x2
yz
= 15x1 + 2
xy1+ 1
z= 15x3
y2
z
Question 4.
Solution:

2. Question 5.
Solution:
Question 6.
Solution:
Question 7.
Solution:
Question 8.

3. Solution:
Find each of the following products : (9-17)
Question 9.
(7ab) x (-5ab2
c) x (6abc2
)
Solution:
(7ab) x (-5ab2
c) x (6abc2
)
= 7 x (-5) x 6 x a x a x a x b x b2
x b x c x c2
=-210 x a1+1+1
x b1+2+1
x c1+2
=-210 x a3
b4
c3
Question 10.
(-5a) x (-10a2
) x (-2a3
)
Solution:
(-5a) x (-10a2
) x (-2a3
)
= (-5) (-10) (-2) x a x a2
x a3
= -100a1 + 2 + 3
= -100a6
Question 11.
(-4x2
) x (-6xy2
) x (-3yz2
)
Solution:
(-4x2
) x (-6xy2
) x (-3yz2
)
= (-4) x (-6) x (-3) x2
x x x y2
x y xz2
= -72x2+1
x y2+1
x z
2
= 72x3
y3
z3
Question 12.

4. Solution:
Question 13.
Solution:
Question 14.
Solution:

5. Question 15.
Solution:
Question 16.
Solution:
Question 17.
(2.3xy) x (0.1x) x (0.16)
Solution:
(2.3xy) x (0.1x) x (0.16)
= 2.3 x 0.1 x 0.16 x x x x x y
= 0.0368x1 +1
x y = 0.0368x2
y
Express each of the following products as a monomials and verify the result in
each case for x = 1 : (18 -26)
Question 18.
(3x) x (4x) x (-5x)

6. Solution:
Question 19.
Solution:
Question 20.
(5x4
) x (x2
)3
x (2x)2

7. Solution:
(5x4
) x (x2
)3
x (2x)2
= 5x4
x x2 x 3
x 2x x 2x
= 5x4
* x6
x 4x2
= 5 x 4 x x4 + 6 + 2
= 20x12
Verification:
L.H.S. = (5x4
) x (x2
)3
x (2x)2
= 5 x (1)4
x [(1)2
]3
x (2 x 1)2
= 5 x 1 x (1)2 x 3
x (2)2
= 5 x 16
x 22
= 5 x 1 x 4 = 20
R.H.S. = 20x12
= 20 (1)12
= 20 x 1 = 20
∴ L.H.S. = R.H.S.
Question 21.
(x2
)3
x (2x) x (-4x) x 5
Solution:
(x2
)3
x (2x) x (-4x) x (5)
= x2 x 3
X 2x X (-4x) X 5
= x6
x 2x x (-4x) x 5 = 2 x (-4) x 5x6+1 +1
= -40x8
Verification
L.H.S. = (x2
)3
x (2x) x (-4x) x (5)
= (12
)3
x (2 x 1) x (-4 x 1) x 5
= 12 x 3
x 2 x (- 4) x 5 = 16
x 2 x (-4) x 5
= 1 x 2 x (-4) x 5 = -40
R.H.S. = -40x8
= -40 x (1)8
= -40 x 1 = -40
∴ L.H.S. = R.H.S.
Question 22.
Write down the product of -8x2
y6
and – 20xy Verify the product for x = 2.5, y = 1.
Solution:
Product of -8x2
y6
and -20xy
= (-8x2
y6
) x (-20xy)
= -8 x (-20) x2
x x x y6
x y = 160x2 + 1
x y6 + 1
= 160x3
y3
Verification.
L.H.S. = (-8x2
y6
) x (-20xy)
= -8 x (2.5)2
x (1) x (-20 x 2.5 x 1)
= -8 x 6.25 x 1 x -20 x 2.5
= (-50) x (-50) = 2500
R.H.S. = 160 x = 160 (2.5)3
x (1)7
= 160 x 15.625 x 1 =2500
∴ L.H.S. = R.H.S.
Question 23.
Evaluate : (3.2x6
y3
) x (2.1x2
y2
) when x = 1 and y = 0.5.
Solution:
3.2x6
y3
x 2.1x2
y2

8. = 3.2 x 2.1 x x6+2
x y3+2
= 6.72x8
y5
= 6.72 x (1)8
x (0.5)5
= 6.72 x 1 x 0.03125
= 0.21
Question 24.
Find the value of (5x6
) x (-1.5x2
y3
) x (-12xy2
) when x = 1, y = 0.5.
Solution:
Question 25.
Evaluate : (2.3a5
b2
) x (1.2a2
b2
) when a = 1, b = 0.5.
Solution:
Question 26.
Evaluate : (-8x2
y6
) x (-20xy) for x = 2.5 and y = 1.

9. Solution:
Express each of the following products as a monomials and verify the result
for x = 1,y = 2: (27-31)
Question 27.
(-xy3
) x (yx3
) x (xy)
Solution:
(-xy3
) x (yx3
) x (xy)
= -x x x3
x x x y3
x y x y = -x1 + 3 + 1
x y3 + 1 + 1
= -x5
y5
Verification:
L.H.S. = (-xy3
) x (yx3
) x (xy)
= (-1 x 23
) x [2 x (1)3
] x (1 X 2)
= (-1 x 8) x (2 x 1) x (1 x 2)
= -8 x 2 x 2 = -32
R.H.S. =-x5
y5
= -(1)5
(2)5
= -1 x 32 =-32
∴ L.H.S. = R.H.S.
Question 28.
Solution:

10. Question 29.
Solution:

11. Question 30.
Solution:
Question 31.
Solution:
Question 32.
Solution:

12. Question 33.
Solution: