Question

Find the value of 297 X 303 by using an appropriate Algebraic identity.​

Answer 1

Given :

• 297 × 303

To Find :

• Value of 297 × 303 using algebraic identity.

Identity Used :

• (a + b)(a - b) = a² - b²

Solution :

⟹ 297 can be written as 300 - 3

⟹ 303 can be written as 300 + 3

⟹ Now, we have got same a and b . Now we will use the identity to find the answer.

⠀⠀

Using Identity :

⟼ (a + b)(a - b) = a² - b²

⟼ (300 + 3)(300 - 3) = a² - b²

⟼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = (300)² - (3)³

⟼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 90000 - 9

⟼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 89,991

Thus The Required answer is 89991

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\small\boxed{\begin{array}{cc}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{array}}$

Answer 2

To Find :- 297 * 303 ?

Solution :-

→ 297 * 303

→ (300 - 3) * (300 + 3)

Let

• 300 = a
• 3 = b .

we know that,

• (a - b) * (a + b) = a² - b²

using this algebraic identity we get,

→ (300)² - (3)²

→ 90000 - 9

→ 89991 (Ans.)

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