# Use the product (a + b)(a - b) = a^2−b^2 to evaluate : (i) 21*19...

Paul Gallegos

## Answered question

2023-02-28

Use the product (a + b)(a - b) = a^2−b^2 to evaluate :

(i) 21*19

(ii) 33*27

(iii) 103*97

(iv) 9.8*10.2

(v) 7.7*8.3

(vi) 4.6*5.4

### Answer & Explanation

$(i)21\times 19=(20+1)(20-1)=(20{)}^{2}-(1{)}^{2}=400-1=399\phantom{\rule{0ex}{0ex}}(ii)33\times 27=(30+3)(30-3)=(30{)}^{2}-(3{)}^{2}=900-1=891\phantom{\rule{0ex}{0ex}}(iii)103\times 97=(100+3)(100-3)=(100{)}^{2}-(3{)}^{2}=10000-9=9991\phantom{\rule{0ex}{0ex}}(iv)9.8\times 10.2=(10-.2)(10-.2)=(10{)}^{2}-(.2{)}^{2}=100-.04=99.96\phantom{\rule{0ex}{0ex}}(v)7.7\times 8.3=(8-.3)(8+.3)=(8{)}^{2}-(.3{)}^{2}=64-.09=63.91\phantom{\rule{0ex}{0ex}}(vi)4.6\times 5.4=(5-.4)(5+.4)=(5{)}^{2}-(.4{)}^{2}=25-.16=24.84$

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