Question

evaluate using the given identity.
${a}^{2} - {b}^{2}$
solve the following
$207 \times 303$
$78 \times 82$
$103 \times 98$
​

Answer 1

$\huge\fbox\red{Question:-}$

evaluate using the given identity.

$\huge({a}^{2} - {b}^{2})$

solve the following

(1)$207 \times 303$

(2)$78 \times 82$

(3)$102 \times 98$

$\huge\fbox\green{Solution:-}$

$(1) \: 207 ×303 \\ we \: know \: that: \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ → (300 + 3)(300 - 3)\\ → {300}^{2} - {3}^{2} \\ → 90000 - 9 \\ = 9991$

$(2)\:78×82 \\we \: know \: that: \\ {a}^{2} - {b}^{2} = (a + b)(a - b)\\ →(80+2)(80-2)\\{80}^{2} - {2}^{2}\\ → 6400 - 4 \\ = 6399$

$(3) \: 102 \times 98 \\ we \: know \: that: \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ →(100 + 2)(100 - 2) \\ → {100}^{2} - {2}^{2} \\ →10000 - 4 \\ =9996$

$\huge\fbox\pink{hope\:it\:helps\:you}$