Intermediate Algebra test 2 review

• True

• False

Answer explanation

The statement $(a+b)^2 = a^2 + b^2$ is false. The correct expansion is $(a+b)^2 = a^2 + 2ab + b^2$, which includes the cross term $2ab$. Therefore, the answer is False.

Tags

CCSS.HSA.APR.C.4

• -1

• 1

• 5

• 0

Answer explanation

The expression -5^0 simplifies to -1 because any non-zero number raised to the power of 0 equals 1. Therefore, -(5^0)=-(1)=-1

Tags

CCSS.8.EE.A.1

Answer explanation

Recall that a negative exponent means "take the reciprocal" Since only x^-4 has a negative exponent, we flip that and bring it to the denominator as x^4.

Tags

CCSS.HSA.APR.A.1

Simplify (a-b)(a+b)

Answer explanation

To simplify (a-b)(a+b), use the difference of squares formula: (x-y)(x+y) = x^2 - y^2. Here, x = a and y = b, so (a-b)(a+b) = a^2 - b^2. Thus, the correct answer is a^2 - b^2.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To multiply, distribute $x^2$ across $x^3 + 5x$: $x^2 \cdot x^3 = x^5$ and $x^2 \cdot 5x = 5x^3$. Thus, the result is $x^5 + 5x^3$, which matches the correct answer.

Tags

CCSS.HSA.APR.A.1

• 5x+6

• 5x+6x

Answer explanation

To divide \( \frac{5x^2 + 6x}{x} \), we can simplify by dividing each term in the numerator by \( x \). This gives us \( 5x + 6 \), making the correct answer \( 5x + 6 \).

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( (3xy^2)^3 \), apply the power of a product rule: \( a^m b^n = a^m \cdot b^n \). Thus, \( 3^3 = 27 \), \( x^1 \) becomes \( x^3 \), and \( (y^2)^3 = y^6 \). Therefore, the result is \( 27x^3y^6 \).

Which of these is the correct expression for:

The length of a rectangle is 3 more than twice the width

• L=W+3

• W=2L+3

• L=2W+3

• W=L+3

Answer explanation

The problem states that the length (L) is 3 more than twice the width (W). This translates to the equation L = 2W + 3, making 'L=2W+3' the correct choice.

Tags

CCSS.6.EE.C.9

When solving two equations with two unknowns, if you end up with an equation such as 0 = 0, what conclusion can you draw?

• There are inf. many solutions.

• There is no solution.

• There is exactly one solution.

• There are two solutions.

Tags

CCSS.8.EE.C.8B

Simplify (x-3)(x+3)

Tags

CCSS.HSA.APR.A.1