Question 21 of 27intermediate🔧 ApplyNumerical4 marks

Compute these products using the suggested identity. (i) 46246^2 using Identity 1A for (a+b)2(a + b)^2 (ii) 397×403397 \times 403 using Identity 1C for (a+b)(a−b)(a + b) (a - b) (iii) 91291^2 using Identity 1B for (a−b)2(a - b)^2 (iv) 43×4543 \times 45 using Identity 1C for (a+b)(a−b)(a + b) (a - b)

(i)
Answer

21162116

(ii)
Answer

159991159991

(iii)
Answer

82818281

(iv)
Answer

19351935

Explanation

(i) (40+6)2=1600+480+36=2116(40 + 6)^2 = 1600 + 480 + 36 = 2116 (ii) (400−3)(400+3)=160000−9=159991(400 - 3)(400 + 3) = 160000 - 9 = 159991 (iii) (100−9)2=10000−1800+81=8281(100 - 9)^2 = 10000 - 1800 + 81 = 8281 (iv) (44−1)(44+1)=1936−1=1935(44 - 1)(44 + 1) = 1936 - 1 = 1935