NCERT Solutions Class 8 Maths Ganita Prakash Chapter 6 We Distribute, Yet Things Multiply on Padhaiwise

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 6 We Distribute, Yet Things Multiply Figure it Out Page 142

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 6 — Figure it Out (Pages 142–143)#

To multiply two expressions, multiply every term of the first by every term of the second, then add the like terms:

$$(a + b)(c + d) = ac + ad + bc + bd$$

1. Observe the multiplication grid below. Each number inside the grid is formed by multiplying two numbers. If the middle number of a 3 × 3 frame is given by the expression pq, as shown in the figure, write the expressions for the other numbers in the grid. #

Solution

The middle number $pq$ is in row $p$ and column $q$. The rows above and below are $p - 1$ and $p + 1$, and the columns to the left and right are $q - 1$ and $q + 1$. (For the frame shown, $p = 4$ and $q = 6$.)

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 6 We Distribute, Yet Things Multiply Figure it Out Page 149

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 6 — Figure it Out (Page 149)#

The identities used here:

1A: $(a + b)^2 = a^2 + 2ab + b^2$
1B: $(a - b)^2 = a^2 - 2ab + b^2$
1C: $(a + b)(a - b) = a^2 - b^2$

1. Which is greater: (a – b)² or (b – a)²? Justify your answer. #

Solution

We expand both using Identity 1B:

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 6 We Distribute, Yet Things Multiply Figure it Out Page 154

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 6 — Figure it Out (Pages 154–156)#

The identities used here:

1A: $(a + b)^2 = a^2 + 2ab + b^2$
1B: $(a - b)^2 = a^2 - 2ab + b^2$
1C: $(a + b)(a - b) = a^2 - b^2$

1. Compute these products using the suggested identity. (i) 46² using Identity 1A for (a + b)² (ii) 397 × 403 using Identity 1C for (a + b) (a – b) (iii) 91² using Identity 1B for (a – b)² (iv) 43 × 45 using Identity 1C for (a + b) (a – b) #

(i) 46²

$$46^2 = (40 + 6)^2$$