Simplify each of the following : (i) 175xx175+2xx175xx25+25xx25 (ii) 322xx322−2xx322xx22+22xx22 (iii) 0.76xx0.76+2xx0.76xx0.24+0.24xx0.24 (iv) (7.83xx7.83−1.17xx1.17)/(6.66)

Taniyah Hartman

Taniyah Hartman

Answered question

2023-01-25

Simplify each of the following : (i) 175 × 175 + 2 × 175 × 25 + 25 × 25 (ii) 322 × 322 2 × 322 × 22 + 22 × 22 (iii) 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × 0.24 (iv) 7.83 × 7.83 1.17 × 1.17 6.66

Answer & Explanation

hemelbol26w

hemelbol26w

Beginner2023-01-26Added 9 answers

(i) 175 × 175 + 2 × 175 × 25 + 25 × 25
Let a=175 and b=25,then
a 2 + 2 a b + b 2 = ( a + b ) 2
= ( 175 + 25 ) 2 = ( 200 ) 2 = 40000
(ii) 322 × 322 2 × 322 × 22 + 22 × 22
Let a=322 and b=22,then
a 2 2 a b + b 2 = ( a b ) 2 = ( 322 22 ) 2 = ( 300 ) 2 = 90000
(iii) 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × 0.24
Let a=0.76 and b=0.24,then
a 2 + 2 a b + b 2 = ( a + b ) 2
= ( 0.76 + 0.24 ) 2 = ( 1.00 ) 2 = 1
(iv) 7.83 × 7.83 1.17 × 1.17 6.66
Let a=7.83,b=1.17,a−b=7.83−1.17=6.66
a × a b × b a b = a 2 b 2 a b
= ( a + b ) ( a b ) a b = a + b
= 7.83 + 1.17 = 9.00 = 9

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