Paul Gallegos

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

Mathew Middleton

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