If the expression 5(x^2 - 2x) - 3(x^2 - 4x) is rewritten in the form ax^2 + bx, where a an… — SAT

If the expression $5(x^2 - 2x) - 3(x^2 - 4x)$ is rewritten in the form $ax^2 + bx$ , where $a$ and $b$ are constants, what is the value of $a$ ?

Answer: 2

The value of

a

2

Distributing the constants outside the parentheses yields

5x^2 - 10x - 3x^2 + 12x

. Combining the

x^2

terms (

5x^2 - 3x^2 = 2x^2

) and the

x

terms (

-10x + 12x = 2x

) gives the simplified equivalent expression

2x^2 + 2x

. Comparing this directly to the form

ax^2 + bx

, we find that the coefficient

a

2

Distribute the coefficients to the terms inside the parentheses.

5x^2 - 10x - 3x^2 + 12x

To expand the expression so that like terms can be combined.

Combine the coefficients of

x^2

and the coefficients of

x

2x^2 + 2x

To write the expression in simplified form.

Identify the value of

a

by matching the simplified expression with

ax^2 + bx

a = 2

The constant

a

represents the coefficient of the

x^2

term.

Simplifying polynomial expressions by distributing constants and combining like terms.

Estimated Time:45s

Question