Which of the following represents the fully simplified form of the expression (3x - 4)^2 -… — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following represents the fully simplified form of the expression $(3x - 4)^2 - x(2x + 5)$ ?

The correct simplified expression is

7x^2 - 29x + 16

Expanding the squared binomial yields

9x^2 - 24x + 16

. Distributing the

-x

yields

-2x^2 - 5x

. Combining the like terms gives

(9x^2 - 2x^2) + (-24x - 5x) + 16

, which simplifies perfectly to

7x^2 - 29x + 16

Expand the squared binomial

(3x - 4)^2

(3x)^2 - 2(3x)(4) + 4^2 = 9x^2 - 24x + 16

Using the perfect square formula

(a - b)^2 = a^2 - 2ab + b^2

is required to properly multiply the binomial by itself.

Distribute the term

-x

across the binomial

(2x + 5)

-x(2x) - x(5) = -2x^2 - 5x

The distributive property must be applied, ensuring the negative sign is carried to both terms inside the parentheses.

Combine the results from the previous steps and combine like terms.

(9x^2 - 24x + 16) + (-2x^2 - 5x) = (9x^2 - 2x^2) + (-24x - 5x) + 16 = 7x^2 - 29x + 16

Like terms (those with the same variable raised to the same power) must be grouped and added together to find the fully simplified polynomial form.

Expanding perfect square binomials and distributing monomial terms correctly.

Question