Ex 4.4, 2

Transcript

Ex 4.4, 2 (i) Select and use the identity that will help you to find the following products without multiplying directly: (i) (41)^2 We can write 41 = 40 + 1 Thus, we use (a + b)2 identity Now, 412 = (40 + 1)2 = 40^2+1^2+2 × 40 × 1 Using (𝑎+𝑏)^2 = 𝑎^2 + 𝑏^2 + 2ab Where 𝑎 = 40, b = 1 = 1,600+1+80 = 𝟏,𝟔𝟖𝟏 Ex 4.4, 2 (ii) Select and use the identity that will help you to find the following products without multiplying directly: (ii) (27)^2 We can write 27 = 30 – 3 Thus, we use (a – b)2 identity Now, 272 = (30 – 3)2 = 30^2+3^2−2 × 30 × 3 Using (𝑎−𝑏)^2 = 𝑎^2 + 𝑏^2 – 2ab Where 𝑎 = 30, b = 3 = 900+9−180 = 909−180 = 𝟕𝟐𝟗 Ex 4.4, 2 (iii) Select and use the identity that will help you to find the following products without multiplying directly: (iii) (23×17) Writing 23 × 17 = (20 + 3) × (20 – 3) So, we can write 𝟐𝟑 × 𝟏𝟕=(20+3) × (20−3) =〖𝟐𝟎〗^𝟐−𝟑^𝟐 =400 −9 =𝟑𝟗𝟏 Using 𝑎^2−𝑏^2=(𝑎 −𝑏)(𝑎+𝑏) Putting 𝒂 = 𝟐𝟎, 𝒃 = 𝟑 Ex 4.4, 2 (iv) Select and use the identity that will help you to find the following products without multiplying directly: (iv) (135)^2 We can write 135 = 100 + 30 + 5 Thus, we use (a + b + c)2 identity Now, 1352 = (100 + 30 + 5)2 =100^2+30^2+5^2+2 × 100 × 30+2 × 100 × 5+2 × 30 × 5 Using (𝑎+𝑏+𝑐)^2=𝑎^2+𝑏^2+𝑐^2+2𝑎𝑏+2𝑏𝑐+2𝑎𝑐 Putting 𝑎 = 100, 𝑏 = 30 & 𝑐 = 5 =10,000+900+25+6,000+1,000+300 =𝟏𝟖,𝟐𝟐𝟓 Ex 4.4, 2 (v) Select and use the identity that will help you to find the following products without multiplying directly: (v) (97)^2 We can write 97 = 100 – 3 Thus, we use (a – b)2 identity Now, 972 = (100 – 3)2 = 100^2+3^2−2 × 100 × 3 Using (𝑎−𝑏)^2 = 𝑎^2 + 𝑏^2 – 2ab Where 𝑎 = 100, b = 3 = 10,000+9−600 = 10,009−600 = 𝟗,𝟒𝟎𝟗 Ex 4.4, 2 (vi) Select and use the identity that will help you to find the following products without multiplying directly: (vi) (18×29) Writing 18 × 29=(20−2) ×(20+9) So, we can write 18 × 29=(20−2) ×(20+9) =〖𝟐𝟎〗^𝟐+(−𝟐+𝟗) × 𝟐𝟎+(−𝟐) × 𝟗 =400+7 × 20−2 × 9 =400+140−18 Using (𝒙+𝒂)(𝒙+𝒃)=𝒙^𝟐+(𝒂+𝒃)𝒙+𝒂𝒃 Putting 𝒙 = 𝟐𝟎 ,𝒂 = −𝟐, 𝒃 = 𝟗 =540−18 =𝟓𝟐𝟐 Ex 4.4, 2 (vii) Select and use the identity that will help you to find the following products without multiplying directly: (vii) (34×43) Writing 18 × 29=(20−2) ×(20+9) So, we can write 18 × 29=(20−2) ×(20+9) =〖𝟐𝟎〗^𝟐+(−𝟐+𝟗) × 𝟐𝟎+(−𝟐) × 𝟗 =400+7 × 20−2 × 9 =400+140−18 Using (𝒙+𝒂)(𝒙+𝒃)=𝒙^𝟐+(𝒂+𝒃)𝒙+𝒂𝒃 Putting 𝒙 = 𝟐𝟎 ,𝒂 = −𝟐, 𝒃 = 𝟗 =540−18 =𝟓𝟐𝟐 Ex 4.4, 2 (viii) Select and use the identity that will help you to find the following products without multiplying directly: (viii) (205)^2 We can write 205 = 200 + 5 Thus, we use (a + b)2 identity Now, 2052 = (200 + 5)2 = 200^2+5^2+2 × 200 × 5 Using (𝑎+𝑏)^2 = 𝑎^2 + 𝑏^2 + 2ab Where 𝑎 = 200, b = 5 = 40,000+25+2,000 = 𝟒𝟐,𝟎𝟐𝟓