Using $a^2 – b^2 = (a + b) (a – b)$, find

(i) ${51}^2– {49}^2$

(ii) ${(1.02)}^2– {(0.98)}^2$

(iii) ${153}^2– {147}^2$

(iv) $12.1^2– 7.9^2$

(i) Given that, ${51}^2– {49}^2$.

We know that $a^2 – b^2 = (a + b) (a – b)$

Apply the above identity for the given expression to get the following,

${51}^2– {49}^2 = (51 + 49)(51 – 49) = 100 \times 2 = 200$

Hence, the value of ${51}^2– {49}^2=200$.

(ii) Given that, ${(1.02)}^2– {(0.98)}^2$.

Apply the above identity for the given expression to get the following,

${(1.02)}^2– {(0.98)}^2 = (1.02 + 0.98)(1.02 – 0.98) = 2 \times 0.04 = 0.08$

Hence, the value of ${(1.02)}^2– {(0.98)}^2=0.08$.

(iii) Given that, ${153}^2– {147}^2$.

Apply the above identity for the given expression to get the following,

${153}^2 – {147}^2 = (153 + 147)(153 – 147) = 300 \times 6 = 1800$

Hence, the value of ${153}^2 -{147}^2=1800$.

(iv) Given that, $12.1^2– 7.9^2$.

Apply the above identity for the given expression to get the following,

$12.1^2 – 7.9^2 = (12.1 + 7.9)(12.1 – 7.9) = 20 \times 4.2= 84$

Hence, the value of $12.1^2– 7.9^2=84$.