If the expression (2x + 3)(3x + 1) - 6x^2 is rewritten in the form bx + c, where b and c a… — SAT

If the expression $(2x + 3)(3x + 1) - 6x^2$ is rewritten in the form $bx + c$ , where $b$ and $c$ are constants, what is the value of $b$ ?

Answer: 11

The value of

b

11

Expanding the expression

(2x + 3)(3x + 1) - 6x^2

yields

(6x^2 + 2x + 9x + 3) - 6x^2

. Combining the linear terms simplifies the expression to

(6x^2 + 11x + 3) - 6x^2

, which further simplifies to

11x + 3

. Comparing this to the form

bx + c

, we see that the coefficient

b

of the

x

term is

11

Expand the product of the binomials

(2x + 3)(3x + 1)

using the distributive property.

6x^2 + 2x + 9x + 3

To rewrite the factored part of the expression in polynomial form.

Combine the linear terms

2x

and

9x

6x^2 + 11x + 3

To simplify the expanded polynomial expression.

Subtract

6x^2

from the simplified polynomial expression.

11x + 3

To complete the subtraction indicated in the original expression.

Compare the resulting expression

11x + 3

to the form

bx + c

to identify the coefficient

b

b = 11

To determine the constant coefficient of the

x

term.

Expanding products of binomials and combining like terms to find equivalent expressions.

Question