Multiplication of Algebraic Expressions

The middle term of the product of ( 2x + 3 ) ( 3x + 2 ) is..................

• 2x

• 12x

• 13x

• 9x

• 7x , 2y , 10xy

• 7x , 3y , 11xy

• 7x , 3y , 21xy

• 7x , 3y , 31xy

The middle term of the product of ( 3b + 5 ) ( 3b - 5 ) = ..............................

• 0

• 25

• 30b

• 2x , 5

• x , 5

• x , -5

Product of 2mn and 6m - 14n is __________.

• 12m²n - 28mn²

• 12m²n - 14n

• 6m²n - 28mn

• 6mn - 14mn²

Answer explanation

2mn x (6m - 14n) Using distributive property of multiplication = (2mn x 6m) - (2mn x 14n) = 2 x 6 x m x m x n - 2 x 14 x m x n x n = 12m²n - 28mn² Therefore, option 1 is correct.

(2x/5 - 3y/7 - 2z/9) (x³/2 - y³/5) = _________________.

• x⁴/5 - 2xy³/25 - 3x³y/14 + 3y⁴/35 - x³y³/7 + y³z/4

• x⁴/4 - 2xy³/25 - 6xy/14 + 3y⁴/35 - x³z/9 + 2y³z/45

• x⁴/5 - 2xy/25 - 4x³y/14 + 3y⁴/35 - x³z/9 + 2y³z/45

• x⁴/5 - 2xy³/25 - 3x³y/14 + 3y⁴/35 - x³z/9 + 2y³z/45

Answer explanation

To find the product we have to multiply each term of first trinomial with each term of the binomial. (2x/5 - 3y/7 - 2z/9) (x³/2 - y³/5) = 2x/5 (x³/2 - y³/5) - 3y/7 (x³/2 - y³/5) - 2z/9 (x³/2 - y³/5) = (2x/5 × x³/2) - (2x/5 × y³/5) - (3y/7 × x³/2) + (3y/7 x y³/5) - (2z/9 x x³/2) + (2z/9 x y³/5) = (2 × x × x³)/(5 x 2) - (2 × x × y³)/(5 × 5) - (3 × y × x³)/(7 × 2) + (3 × y × y³)/(7 × 5) - (2 × z × x³)/(9 × 2) + (2 × z × y³)/(9 × 5) = x⁴/5 - 2xy³/25 - 3x³y/14 + 3y⁴/35 - x³z/9 + 2y³z/45 Therefore, option 4 is correct.

If a monomial is multiplied with a monomial, then the result will be _________.

• a monomial

• a binomial

• a trinomial

• polynomial with more than one term

Answer explanation

If a monomial is multiplied with a monomial, then the result will be a monomial. Therefore, option 1 is correct.

The product of (3ab - 5)(4a + 3) contains _________.

• one constant term

• two constant terms

• three constant terms

• four constant terms

Answer explanation

To multiply a binomial by a binomial, every term in one binomial is multiplied with every term in the other binomial. (3ab - 5)(4a + 3) = 3ab(4a + 3) -5(4a + 3) = (3ab x 4a) + (3ab x 3) - (5 x 4a) - (5 x 3) = 12a²b + 9ab - 20a - 15 As we can see there is only one constant term in the product, hence option 1 is correct. Alternatively, one can think that a constant term can be obtained by multiplying -5 with 3 only. In none of the other cases we can get a constant term. Hence option 1 is the correct answer.

Area of a rectangle with length (m + 4n) and breadth (3n + 5m) is given by __________.

• 23mn + 5m + 9n

• 5m² + 23mn + 12n²

• 23m²n² + 5m² + 9n²

• 12m² + 23mn + 5n²

Answer explanation

Area of a rectangle = length x breadth Here, length = (m + 4n) and breadth = (3n + 5m) So, Area of rectangle = (m + 4n)(3n + 5m) To multiply a binomial by binomial, we multiply each term of one binomial with each term of the other binomial. (m + 4n)(3n + 5m) = m (3n + 5m) + 4n(3n + 5m) = (m x 3n) + (m x 5m) + (4n x 3n) + (4n x 5m) = 3mn + 5m² + 12n² + 20mn = (3mn + 20mn) + 5m² + 12n² = 23mn + 5m² + 12n² Therefore, option 2 is correct.

Simplify: (1.1a – 3b)(1.5a + 5b - 2.5) – (2.6a × 1.2b) - 8b

• 2.6a² + 7.2a²b - 2.5ab - 0.5b

• 1.65a² + 12ab - 0.75a - 2b

• 12.88ab - 2.5ab - 3.5b² - a² - 1.3b²

• 1.65a² -15b² - 2.12ab - 2.75a - 0.5b

Answer explanation

(1.1a – 3b)(1.5a + 5b - 2.5) – (2.6a × 1.2b) - 8b = 1.1a (1.5a + 5b - 2.5) - 3b (1.5a + 5b - 2.5) - (2.6 x 1.2 x a x b) - 8b = (1.1a x 1.5a) + (1.1a x 5b) - (1.1a x 2.5) - (3b x 1.5a) - (3b x 5b) + (3b x 2.5) - 3.12ab - 8b = 1.65a² + 5.5ab - 2.75a - 4.5ab - 15b² + 7.5b - 3.12ab - 8b = 1.65a² + 5.5ab + (-2.75a) + (-4.5ab) + (-15b²) + 7.5b + (-3.12ab) + (-8b) = 1.65a² + [{5.5ab + (-4.5ab)} + (-3.12ab)] + (-2.75a) + (-15b²) + {7.5b + (-8b)} (using commutative and associative properties of addition) = 1.65a² + [ab + (-3.12ab)] + (-2.75a) + (-15b²) + (-0.5b) = 1.65a² + (-2.12ab) + (-2.75a) + (-15b²) + (-0.5b) = 1.65a² + (-15b²) + (-2.12ab) + (-2.75a) + (-0.5b) which can also be written as = 1.65a² -15b² - 2.12ab - 2.75a - 0.5b Therefore, option 4 is correct.