Question

Factor 81x^2-100 A (9x-10)(9x-10) B (9x+10)(9x+10) C (9x+10)(9x-10) D (9x+50)(9x-50)

Answer 1

Here, we are having a quadratic equation in one variable because the highest degree is 2 and contains only one variable i.e. x

Given, equation:

$81 {x}^{2} - 100$

Now, if we observe the terms used in the polynomial, 81x² and 100 separated by a negative sign, we can analyze and can factorise using the identity:

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

Consider:

• a² = 81x²
• b² = 100

So, let's factorise by using the above identity

$81 {x}^{2} - 100$

$(9x) {}^{2} - (10) {}^{2}$

Here, a = 9x and b = 10,

$(9x + 10)(9x - 10)$

Is the factorised form of 81x² - 100

So Correct Option is: Option C

━━━━━━━━━━━━━━━━━━━━