Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

We want to factor the following expression:

(x+5)^(4)+2(x+5)^(2)-1
Which pattern can we use to factor the expression?

U and
V are either constant integers or single-variable expressions.
Choose 1 answer:
(A)
(U+V)^(2) or
(U-V)^(2)
(B)
(U+V)(U-V)
(c) We can't use any of the patterns.

We want to factor the following expression: $\newline$ $(x+5)^{4}+2(x+5)^{2}-1$ $\newline$ Which pattern can we use to factor the expression? $\newline$ $U$ and $V$ are either constant integers or single-variable expressions. $\newline$ Choose $1$ answer: $\newline$ (A) $(U+V)^{2}$ or $(U-V)^{2}$ $\newline$ (B) $(U+V)(U-V)$ $\newline$ (C) We can't use any of the patterns.

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q. We want to factor the following expression:

\newline

(x+5)^{4}+2(x+5)^{2}-1

\newline

Which pattern can we use to factor the expression?

\newline

U

and

V

are either constant integers or single-variable expressions.

\newline

Choose

1

answer:

\newline

(A)

(U+V)^{2}

or

(U-V)^{2}

\newline

(B)

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Recognize the structure: Recognize the structure of the given expression. $\newline$ The given expression is $(x+5)^{4}+2(x+5)^{2}-1$ . We can see that it resembles a quadratic in form, where $(x+5)^{2}$ can be considered as a single variable, let's call it $U$ . So the expression can be rewritten as $U^{2} + 2U - 1$ , where $U = (x+5)^{2}$ .
Identify the factoring pattern: Identify the factoring pattern. $\newline$ The rewritten expression $U^2 + 2U - 1$ is a quadratic expression and does not fit the perfect square patterns $(U+V)^{2}$ or $(U-V)^{2}$ , nor does it fit the difference of squares pattern $(U+V)(U-V)$ . However, it can be factored using the methods for factoring a quadratic expression, which is not listed in the given choices.
Determine if given patterns apply: Determine if any of the given patterns apply. $\newline$ Since the expression is a quadratic in $U$ and does not fit the given patterns $(A)$ or $(B)$ , and since we can factor it using methods for factoring quadratics, the correct answer is $(C)$ We can't use any of the patterns.

More problems from Compare linear and exponential growth

Question

We want to factor the following expression:

\newline

x^{4}+10 x+25

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

(x-2)^{4}-(y+3)^{4}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

(x-1)^{2}+(x-1)+4

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

9 x^{4}+4 y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

16 x^{4}-25

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

x^{4}+3 x^{2} y+9 y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

(x-3)^{2}-10(x-3)+25

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

(x+7)^{2}+2 y(x+7)+y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

We want to factor the following expression:

\newline

9 x^{6}+6 x^{3} y+y^{2}

\newline

Which pattern can we use to factor the expression?

\newline

U

V

are either constant integers or single-variable expressions.

\newline

1

\newline

(U+V)^{2}

(U-V)^{2}

\newline

(U+V)(U-V)

\newline

(C) We can't use any of the patterns.

Posted 8 months ago

Question

Jonah measured a summer camp and made a scale drawing. In real life, the sand volleyball court is

8

meters wide. It is

2

centimeters wide in the drawing. What is the scale factor of the drawing? Simplify your answer and write it as a fraction.

Posted 1 hour ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant