MULTIPLYING ALGEBRAIC TERMS AND EXPRESSIONS

Problem 1 :

What is the power of X in the product of X × X.

a)  4    b)  2      c)  3     d)  None of these

Solution :

Product of X × X = X²

 The power of X = 2

So, option (b) is correct.

Problem 2 :

Z × (3 + Z) = ______

Solution :

= Z × (3 + Z)

= Z × 3 + Z × Z

= 3Z + Z²

Problem 3 :

Find the product, 4X × 3Y × 5.

Solution :

= 4X × 3Y × 5

= 60XY

Problem 4 :

Find the product, (3x + 2) (5)

Solution :

= (3x + 2) × (5)

= 15x + 10

Problem 5 :

4.1X × 3.4Y × 5.6Z find the product.

Solution :

= 4.1X × 3.4Y × 5.6Z

= 78.064 XYZ

Problem 6 :

Find the product of 4x × 0 × 24y

Solution :

= 4x × 0 × 24y

= 0

Always the product of any number and zero will be zero.

Problem 7 :

Solve the following (3x + 7) (2y + 1)

Solution :

= (3x + 7) (2y + 1)

= 3x (2y + 1) + 7(2y + 1)

= 6xy + 3x + 14y + 7

Problem 8 :

Find the product (3x + 2) (5 + 2x)

Solution :

= (3x + 2) (5 + 2x)

= 3x (5 + 2x) + 2 (5 + 2x)

= 15x + 6x² + 10 + 4x

= 6x² + 19x + 10

Problem 9 :

Find the product of

(3x + 2) and (5 + 2xy + x)

and write number of terms after multiplication.

Solution :

= (3x + 2) (5 + 2xy + x)

= 3x (5 + 2xy + x) + 2 (5 + 2xy + x)

= 15x + 6x²y + 3x² + 10 + 4xy + 2x

= 17x + 6x²y + 3x² + 10 + 4xy

There are 5 terms.

Problem 10 :

Write the product of variables in the expression

3x + 5yz + 7x²

Solution :

Variables = x, yz, x²

Product of variables = x × yz × x²

= x³yz

Problem 11 :

Find the product of (3x + 12y²) and (5 + 2xy + x)

Solution :

= (3x + 12y²) (5 + 2xy + x)

= 3x (5 + 2xy + x) + 12y² (5 + 2xy + x)

= 15x + 6x²y + 3x² + 60y² + 24xy³ + 12xy²

Problem 12 :

Z × (3 + 4Z) = ______

Solution :

= Z × (3 + 4Z)

= Z × 3 + Z × 4Z

= 3Z + 4Z²