Math / Algebra

QuestionQuestion 4 of 17
Factor the polynomial if it is a perfect square trinomial, or state that the polynomial is prime. $x^{2}-20 x y+100 y^{2}$
Select the correct choice below and fill in any answer boxes within your choice. A. $x^{2}-20 x y+100 y^{2}=$ $\square$ B. The polynomial is prime.

Studdy Solution

STEP 1

1. A perfect square trinomial takes the form $(a-b)^2 = a^2 - 2ab + b^2$ .
2. We need to determine if the given polynomial fits this form.
3. If it does, we will factor it; otherwise, we will state that it is prime.

STEP 2

1. Identify the structure of the polynomial.
2. Determine if the polynomial is a perfect square trinomial.
3. Factor the polynomial if it is a perfect square trinomial.

STEP 3

Identify the terms in the polynomial $x^{2}-20xy+100y^{2}$ .
- The first term is $x^2$ , which is a perfect square $(x)^2$ . - The last term is $100y^2$ , which is a perfect square $(10y)^2$ .

STEP 4

Check if the middle term fits the form $-2ab$ , where $a = x$ and $b = 10y$ .
- Calculate $2ab = 2 \times x \times 10y = 20xy$ .
The middle term $-20xy$ matches $-2ab$ .

STEP 5

Since the polynomial fits the form of a perfect square trinomial, factor it as:
$(x - 10y)^2$
Thus, the factored form of the polynomial is:
$x^{2}-20xy+100y^{2} = (x - 10y)^2$

Was this helpful?

QuestionQuestion 4 of 17
Factor the polynomial if it is a perfect square trinomial, or state that the polynomial is prime. $x^{2}-20 x y+100 y^{2}$
Select the correct choice below and fill in any answer boxes within your choice. A. $x^{2}-20 x y+100 y^{2}=$ $\square$ B. The polynomial is prime.

Studdy Solution

STEP 1

1. A perfect square trinomial takes the form $(a-b)^2 = a^2 - 2ab + b^2$ .
2. We need to determine if the given polynomial fits this form.
3. If it does, we will factor it; otherwise, we will state that it is prime.

STEP 2

1. Identify the structure of the polynomial.
2. Determine if the polynomial is a perfect square trinomial.
3. Factor the polynomial if it is a perfect square trinomial.

STEP 3

Identify the terms in the polynomial $x^{2}-20xy+100y^{2}$ .
- The first term is $x^2$ , which is a perfect square $(x)^2$ . - The last term is $100y^2$ , which is a perfect square $(10y)^2$ .

STEP 4

Check if the middle term fits the form $-2ab$ , where $a = x$ and $b = 10y$ .
- Calculate $2ab = 2 \times x \times 10y = 20xy$ .
The middle term $-20xy$ matches $-2ab$ .

STEP 5

Since the polynomial fits the form of a perfect square trinomial, factor it as:
$(x - 10y)^2$
Thus, the factored form of the polynomial is:
$x^{2}-20xy+100y^{2} = (x - 10y)^2$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

1. A perfect square trinomial takes the form (a−b)2=a2−2ab+b2(a-b)^2 = a^2 - 2ab + b^2(a−b)2=a2−2ab+b2.2. We need to determine if the given polynomial fits this form.3. If it does, we will factor it; otherwise, we will state that it is prime.

STEP 2

1. Identify the structure of the polynomial.2. Determine if the polynomial is a perfect square trinomial.3. Factor the polynomial if it is a perfect square trinomial.

STEP 3

Identify the terms in the polynomial x2−20xy+100y2x^{2}-20xy+100y^{2}x2−20xy+100y2.- The first term is x2x^2x2, which is a perfect square (x)2(x)^2(x)2. - The last term is 100y2100y^2100y2, which is a perfect square (10y)2(10y)^2(10y)2.

STEP 4

Check if the middle term fits the form −2ab-2ab−2ab, where a=xa = xa=x and b=10yb = 10yb=10y.- Calculate 2ab=2×x×10y=20xy2ab = 2 \times x \times 10y = 20xy2ab=2×x×10y=20xy.The middle term −20xy-20xy−20xy matches −2ab-2ab−2ab.

STEP 5

Since the polynomial fits the form of a perfect square trinomial, factor it as:(x−10y)2(x - 10y)^2(x−10y)2Thus, the factored form of the polynomial is:x2−20xy+100y2=(x−10y)2x^{2}-20xy+100y^{2} = (x - 10y)^2x2−20xy+100y2=(x−10y)2

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. A perfect square trinomial takes the form $(a-b)^2 = a^2 - 2ab + b^2$ .
2. We need to determine if the given polynomial fits this form.
3. If it does, we will factor it; otherwise, we will state that it is prime.

1. Identify the structure of the polynomial.
2. Determine if the polynomial is a perfect square trinomial.
3. Factor the polynomial if it is a perfect square trinomial.

Identify the terms in the polynomial $x^{2}-20xy+100y^{2}$ .
- The first term is $x^2$ , which is a perfect square $(x)^2$ . - The last term is $100y^2$ , which is a perfect square $(10y)^2$ .

Check if the middle term fits the form $-2ab$ , where $a = x$ and $b = 10y$ .
- Calculate $2ab = 2 \times x \times 10y = 20xy$ .
The middle term $-20xy$ matches $-2ab$ .

Since the polynomial fits the form of a perfect square trinomial, factor it as:
$(x - 10y)^2$
Thus, the factored form of the polynomial is:
$x^{2}-20xy+100y^{2} = (x - 10y)^2$