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(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.

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

  • (3x − 2)(3x + 2) = ax2 − b⠀⠀⠀⠀

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

  • ⠀what is the value of a?⠀⠀⠀

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

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

  • [tex]\sf{(3x-2)(3x+2) }[/tex]

  • [tex]\sf{3x(3x+2)-2(3x+2) }[/tex]

  • [tex]\sf{9x^{2}+6x-6x-4 }[/tex]

  • [tex]\sf{9x^{2}-4 }[/tex]

According to the question,

  • [tex]\sf{ (3x − 2)(3x + 2) = ax^{2} − b }[/tex]

  • [tex]\sf{9x^{2}-4=ax^{2}-b }[/tex]

  • [tex]\sf{9x^{2}=ax^{2}~and~-4=-b }[/tex]

  • [tex]\sf{a=9~and~b=4 }[/tex]

⠀⠀⠀

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

Hence,

The value of a is 9

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