Short Question Answer: We Distribute, Yet Things Multiply | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Q1: Write two examples of each of:
(i) Monomials
(ii) Binomials
(iii) Trinomials

Ans: 
(i) Monomials:
(a) 7x
(b) -62xy²

(ii) Binomials:
(a) 4p + q
(b) -75a + 42b

(iii) Trinomials:
(a) a + b + c
(b) x² - 45x + 2

Q2: Add the following : 
(a) 9x²−6x+7 and 5x²+4x−3.
(b) 7x²+3x−5 and 4x²−2x+6.

Ans: 
(a) 

The sum is 14x²−2x+4.

(b)

The sum is 11x²+x+1.

Q2: Multiply (6x² – 5x + 3) by (3x² + 7x – 3)
Ans: (6x² – 5x + 3) × (3x² + 7x – 3)
= 6x²(3x² + 7x – 3) – 5x(3x² + 7x – 3) + 3(3x² + 7x – 3)
= 18x⁴ + 42x³ – 18x² – 15x³ – 35x² + 15x + 9x² + 21x – 9
= 18x⁴ + 42x³ – 15x³ – 18x² – 35x² + 9x² + 15x + 21x – 9
= 18x⁴ + 27x³ – 44x² + 36x – 9

Q3:  Multiply (3x² + 5y²) by (5x² – 3y²)
Ans: (3x² + 5y²) × (5x² – 3y²)
= 3x²(5x² – 3y²) + 5y²(5x² – 3y²)
= 15x⁴ – 9x²y² + 25x²y² – 15y⁴
= 15x⁴ + 16x²y² – 15y⁴

Q4: Subtract the following :

(a) 4x⁴−3x³+5x²−2x+7 from 5x⁴−6x³+4x²−x+9.
(b) 3x⁵−4x⁴+6x³−2x²+x−5 from 5x⁵−3x⁴+2x³−x²+4x+7.
Ans: 
(a) 

(b) 

Q5:  Find the product of the following pairs of monomials.

(i) 3x,5y
(ii) −6x,2x²
(iii) −7x,−3x³
(iv) 4xy,−2y²
(v) 5x²y,0
Ans: 
$\mathrm{<strong\; style="box-sizing:\; border-box;\; font-family:\; Lato,\; sans-serif;\; letter-spacing:\; inherit;\; font-weight:\; 700;\; word-break:\; break-word;\; font-size:\; 20px;\; color:\; black;\; line-height:\; 1.8;">(i) </strong>}$3x × 5y = (3 × 5)×(x × y) = 15xy
(ii)−6x × 2x² = (−6 × 2) × (x × x²) = −12x³ 
(iii) −7x × −3 x 3 = (−7 × −3) × (x × x³) = 21x⁴
(iv) 4xy × −2y² = (4 × −2) × (xy × y²) = −8xy³
(v) 5x²y × 0 = 5 × x²y × 0 = 0

Q6: Simplify: 2x²(x + 2) – 3x (x² – 3) – 5x(x + 5)
Ans: 2x²(x + 2) – 3x(x² – 3) – 5x(x + 5)
= 2x³ + 4x² – 3x³ + 9x – 5x² – 25x
= 2x³ – 3x³ – 5x² + 4x² + 9x – 25x
= -x³ – x² – 16x

Q7: Simplify the following :
(i) (y²−4) (y + 3) + 12
(ii) (m²+6)(n³−2)+7
Ans:  (i) Simplifying (y²−4) (y + 3) + 12

(ii) Simplifying (m²+6)(n³−2)+7
​

Q8: Identify the like expressions:
7a, −2a, 4b², −6b², ab, −3ab
Ans: Like terms:

• 7a and −2a
• 4b² and −6b²
• ab and −3ab

Q9: Find the area of the rectangle whose length and breadth are 4x²y  m and7xy³  m respectively.
Ans: 

Q10. The cost of painting a rectangular board is calculated based on its area. If the length of the board is  5x³y² m and the breadth is3xy³  m, find the area of the board to estimate the cost of painting.

Ans: