Question

If (3x − 2)(3x + 2) = ax2 − b, what is the value of a?

Answer 1

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

• (3x − 2)(3x + 2) = ax2 − b⠀⠀⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

• ⠀what is the value of a?⠀⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

At first we have to solve the value of (3x-2)(3x+2)

• $\sf{(3x-2)(3x+2) }$

• $\sf{3x(3x+2)-2(3x+2) }$

• $\sf{9x^{2}+6x-6x-4 }$

• $\sf{9x^{2}-4 }$

According to the question,

• $\sf{ (3x − 2)(3x + 2) = ax^{2} − b }$

• $\sf{9x^{2}-4=ax^{2}-b }$

• $\sf{9x^{2}=ax^{2}~and~-4=-b }$

• $\sf{a=9~and~b=4 }$

⠀⠀⠀

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

Hence,

The value of a is 9

Answer 2

(3x-2)(3x+ 2)

Multiply each term in one set of parentheses by the other terms:

3x x 3x =9x^2

3x x 2 = 6x

-2 x 3x = -6x

-2 x 2 = -4

Combine to get:

9x^2 + 6x - 6x -4

Combine like terms:

9x^2 - 4

The value of a would be 9.