Ex 4.3, 1

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Ex 4.3, 1 (i) Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. (i) 117^2 We can write 117 = 120 – 3 Thus, we use (a – b)2 identity Now, 1172 = (120 – 3)2 = 120^2+3^2−2 × 120 × 3 Using (𝑎−𝑏)^2 = 𝑎^2 + 𝑏^2 – 2ab Where 𝑎 = 120, b = 3 = 14,400+9−720 = 14,409−720 = 𝟏𝟑,𝟔𝟖𝟗 Ex 4.3, 1 (ii) Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. (ii) 78^2 We can write 78 = 80 – 2 Thus, we use (a – b)2 identity Now, 782 = (80 – 2)2 = 80^2+2^2−2 × 80 × 2 Using (𝑎−𝑏)^2 = 𝑎^2 + 𝑏^2 – 2ab Where 𝑎 = 80, b = 2 = 6,400+4−320 = 6,404−320 = 𝟔,𝟎𝟖𝟒 Ex 4.3, 1 (iii) Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. (iii) 198^2 We can write 198 = 200 – 2 Thus, we use (a – b)2 identity Now, 1982 = (200 – 2)2 = 200^2+2^2−2 × 200 × 2 Using (𝑎−𝑏)^2 = 𝑎^2 + 𝑏^2 – 2ab Where 𝑎 = 200, b = 2 = 40,000+4−800 = 40,004−800 = 𝟑𝟗,𝟐𝟎𝟒 Ex 4.3, 1 (iv) Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. (iv) 214^2 We can write 214 = 200 + 10 + 4 Thus, we use (a + b + c)2 identity Now, 2142 = (200 + 10 + 4)2 =200^2+10^2+4^2+2 × 200 × 10+2 × 200 × 4+2 × 10 × 4 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 200, 𝑏 = 10 & 𝑐 = 4 =40,000+100+16+4,000+1,600+80 =𝟒𝟓,𝟕𝟗𝟔 Ex 4.3, 1 (v) Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. (v) 1104^2 We can write 1104 = 1000 + 100 + 4 Thus, we use (a + b + c)2 identity Now, 11042 = (1000 + 100 + 4)2 =1,000^2+100^2+4^2+2 × 1,000 × 100+2 × 1,000 × 4+2 × 100 × 4 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 1000, 𝑏 = 100 & 𝑐 = 4 =10,00,000+10,000+16+2,00,000+8,000+800 =𝟏𝟐,𝟏𝟖,𝟖𝟏𝟔 Ex 4.3, 1 (vi) Find the following squares using one of the above identities. Determine which of these identities will make these calculations easier. (vi) 1120^2 We can write 1104 = 1000 + 100 + 20 Thus, we use (a + b + c)2 identity Now, 11042 = (1000 + 100 + 20)2 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 1000, 𝑏 = 100 & 𝑐 = 20 =1,000^2+100^2+20^2+2 × 1,000 × 100+2 × 1,000 × 20+2 × 100 × 20 =10,00,000+10,000+400+2,00,000+40,000+4,000 =𝟏𝟐,𝟓𝟒,𝟒𝟎𝟎