Use the product a - ba - b - a2 - b2 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

(i) 21 × 19 = (20 + 1) (20 1) = (20)^2 (1)^2 = 400 1 = 399 (ii) 33 × 27 = (30 + 3) (30 3) = (30)^2 (3)^2 = 900 1 = 891 (iii) 103 × 97 = (100 + 3) (1 ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (x^2 - y^2)

Use the produ...

Question

Use the product (a + b)(a - b) = $a^{2} - b^{2}$ to evaluate :

(i) $21 \times 19$

(ii) $33 \times 27$

(iii) $103 \times 97$

(iv) $9.8 \times 10.2$

(v) $7.7 \times 8.3$

(vi) $4.6 \times 5.4$

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Solution

(i) $21 \times 19 = (20 + 1) (20 - 1) = (20)^{2} - (1)^{2} = 400 - 1 = 399$

(ii) $33 \times 27 = (30 + 3) (30 - 3) = (30)^{2} - (3)^{2} = 900 - 1 = 891$

(iii) $103 \times 97 = (100 + 3) (100 - 3) = (100)^{2} - (3)^{2} = 10000 - 9 = 9991$

(iv) $9.8 \times 10.2 = (10 - .2) (10 - .2) = (10)^{2} - (.2)^{2} = 100 - .04 = 99.96$

(v) $7.7 \times 8.3 = (8 - .3) (8 + .3) = (8)^{2} - (.3)^{2} = 64 - .09 = 63.91$

(vi) $4.6 \times 5.4 = (5 - .4) (5 + .4) = (5)^{2} - (.4)^{2} = 25 - .16 = 24.84$

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Use the product (a + b)(a - b) = a2−b2 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

Use the product (a + b)(a - b) = $a^{2} - b^{2}$ to evaluate :

(i) $21 \times 19$

(ii) $33 \times 27$

(iii) $103 \times 97$

(iv) $9.8 \times 10.2$

(v) $7.7 \times 8.3$

(vi) $4.6 \times 5.4$