The expression (2y - 7)^2 is expanded into the standard polynomial form ay^2 + by + c. Wha… — Armed Services Vocational Aptitude Battery (ASVAB)

The expression $(2y - 7)^2$ is expanded into the standard polynomial form $ay^2 + by + c$ . What is the value of the coefficient $b$ ?

Answer: -28

Answer

-28

Expanding the perfect square binomial

(2y - 7)^2

requires multiplying

(2y - 7)

by itself. Using the distributive property, the outer product is

(2y)(-7) = -14y

and the inner product is

(-7)(2y) = -14y

. Combining these like terms gives a total middle term of

-28y

. Because the required polynomial form is

ay^2 + by + c

, the value of the coefficient

b

is exactly -28.

Step-by-Step Solution

Rewrite the expression as a product of two binomials.

(2y - 7)(2y - 7)

Writing the binomial twice makes it easier to correctly apply the distributive property (FOIL method) and avoid missing the middle terms.

Distribute the terms.

4y^2 - 14y - 14y + 49

Multiplying the First terms, Outer terms, Inner terms, and Last terms ensures that every term in the first binomial is multiplied by every term in the second binomial.

Combine the like terms.

4y^2 - 28y + 49

The middle terms,

-14y

and

-14y

, have the same variable raised to the same power, so their coefficients can be added together.

Identify the target coefficient.

-28

The standard polynomial form is given as

ay^2 + by + c

. The value of

b

corresponds to the coefficient of the

y

term.

Key Concept

Expanding Perfect Square Binomials

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic