Simplify the following using the formula: $(a - b) (a + b) = a^{2} - b^{2} :$

$(i) (82)^{2} - (18)^{2}$ $(i i) (467)^{2} - (33)^{2}$ $(i i i) (79)^{2} - (69)^{2}$ $(i v) 197 \times 203$

$(v) 113 \times 87$ $(v i) 95 \times 105$ $(v i i) 1.8 \times 2.2$ $(v i i i) 9.8 \times 10.2$

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Solution

$(i) (82)^{2} - (18)^{2} = (82 + 18) (82 - 18) {(a + b) (a - b) = a^{2} - b^{2}} = 100 \times 64 = 6400 (i i) (467)^{2} - (33)^{2} = (467 + 33) (467 - 33) = 500 \times 434 = 217000 (i i i) (79)^{2} - (69)^{2} = (79 + 69) (79 - 69) = 148 \times 10 = 1480 (i v) 197 \times 203 = (200 - 3) (200 + 3) = (200)^{2} - (3)^{2} = 40000 - 9 = 39991 (v) 113 \times 87 = (100 + 13) (100 - 13) = (100)^{2} - (13)^{2} = 10000 - 169 = 9831 (v i) 95 \times 105 = (100 - 5) (100 + 5) = (100)^{2} - (5)^{2} = 10000 - 25 = 9975 (v i i) 1.8 \times 2.2 = (2.0 - 0.2) (2.0 + 0.2) = (2.0)^{2} - (0.2)^{2} = 4.00 - 0.04 = 3.96 (v i i i) 9.8 \times 10.2 = (10.0 - 0.2) (10.0 + 0.2) (10.0)^{2} - (0.2)^{2} = 100.00 - 0.04 = 99.96$

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Similar questions

Q. Simplify the following using the formula:

(a - b) (a + b) = a^{2} - b^{2}

(i)

(82)^{2} - (18)^{2}

(ii)

(467)^{2} - (33)^{2}

(iii)

(79)^{2} - (69)^{2}

Q. Use the identity

(a + b) (a - b) = a^{2} - b^{2}

to evaluate:

9.8 \times 10.2

Q. Find the value of:
(i) (82)² − (18)²
(ii) (128)² − (72)²
(iii) 197 × 203
(iv)

\frac{198 \times 198 - 102 \times 102}{96}

(v) (14.7 × 15.3)
(vi) (8.63)² − (1.37)²

Find the values of
(i) $(82)^{2} - (18)^{2}$
(ii) $(128)^{2} - (72)^{2}$
(iii) $197 \times 203$
(iv) $\frac{198 \times 198 - 102 \times 102}{96}$
(v) $(14.7 \times 15.3)$
(vi) $(8.63)^{2} - (1.37)^{2}$

Q. Use the formula :

(a + b) (a - b) = a^{2} - b^{2}

to evaluate :

7.7 \times 8.3

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Simplify the following using the formula: (a−b)(a+b)=a2−b2: (i) (82)2−(18)2 (ii) (467)2−(33)2 (iii) (79)2−(69)2 (iv) 197×203 (v) 113×87 (vi) 95×105 (vii) 1.8×2.2 (viii) 9.8×10.2

Simplify the following using the formula: $(a - b) (a + b) = a^{2} - b^{2} :$

$(i) (82)^{2} - (18)^{2}$ $(i i) (467)^{2} - (33)^{2}$ $(i i i) (79)^{2} - (69)^{2}$ $(i v) 197 \times 203$

$(v) 113 \times 87$ $(v i) 95 \times 105$ $(v i i) 1.8 \times 2.2$ $(v i i i) 9.8 \times 10.2$