Math / Algebra

QuestionQuestion Watcl
Expand and state your answer as a polynomial in standard form. $\left(5 x+y^{3}\right)^{2}$
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

1. We need to expand the expression $(5x + y^3)^2$ .
2. The expansion will use the formula for the square of a binomial.
3. The result should be expressed as a polynomial in standard form.

STEP 2

1. Apply the formula for the square of a binomial.
2. Simplify the expanded terms.
3. Write the polynomial in standard form.

STEP 3

Apply the formula for the square of a binomial $(a + b)^2 = a^2 + 2ab + b^2$ to the expression $(5x + y^3)^2$ .
Here, $a = 5x$ and $b = y^3$ .
$(5x + y^3)^2 = (5x)^2 + 2(5x)(y^3) + (y^3)^2$

STEP 4

Calculate each term in the expansion:
1. $(5x)^2 = 25x^2$
2. $2(5x)(y^3) = 10xy^3$
3. $(y^3)^2 = y^6$

STEP 5

Combine the terms to form the expanded polynomial:
$25x^2 + 10xy^3 + y^6$

STEP 6

Write the polynomial in standard form, which is already achieved as:
$y^6 + 10xy^3 + 25x^2$
The polynomial in standard form is:
$\boxed{y^6 + 10xy^3 + 25x^2}$

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QuestionQuestion Watcl
Expand and state your answer as a polynomial in standard form. $\left(5 x+y^{3}\right)^{2}$
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

1. We need to expand the expression $(5x + y^3)^2$ .
2. The expansion will use the formula for the square of a binomial.
3. The result should be expressed as a polynomial in standard form.

STEP 2

1. Apply the formula for the square of a binomial.
2. Simplify the expanded terms.
3. Write the polynomial in standard form.

STEP 3

Apply the formula for the square of a binomial $(a + b)^2 = a^2 + 2ab + b^2$ to the expression $(5x + y^3)^2$ .
Here, $a = 5x$ and $b = y^3$ .
$(5x + y^3)^2 = (5x)^2 + 2(5x)(y^3) + (y^3)^2$

STEP 4

Calculate each term in the expansion:
1. $(5x)^2 = 25x^2$
2. $2(5x)(y^3) = 10xy^3$
3. $(y^3)^2 = y^6$

STEP 5

Combine the terms to form the expanded polynomial:
$25x^2 + 10xy^3 + y^6$

STEP 6

Write the polynomial in standard form, which is already achieved as:
$y^6 + 10xy^3 + 25x^2$
The polynomial in standard form is:
$\boxed{y^6 + 10xy^3 + 25x^2}$

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QuestionQuestion WatclExpand and state your answer as a polynomial in standard form. (5x+y3)2\left(5 x+y^{3}\right)^{2}(5x+y3)2Answer Attempt 1 out of 2

Studdy Solution

STEP 1

1. We need to expand the expression (5x+y3)2(5x + y^3)^2(5x+y3)2.2. The expansion will use the formula for the square of a binomial.3. The result should be expressed as a polynomial in standard form.

STEP 2

1. Apply the formula for the square of a binomial.2. Simplify the expanded terms.3. Write the polynomial in standard form.

STEP 3

STEP 4

Calculate each term in the expansion:1. (5x)2=25x2(5x)^2 = 25x^2(5x)2=25x22. 2(5x)(y3)=10xy32(5x)(y^3) = 10xy^32(5x)(y3)=10xy33. (y3)2=y6(y^3)^2 = y^6(y3)2=y6

STEP 5

Combine the terms to form the expanded polynomial:25x2+10xy3+y6 25x^2 + 10xy^3 + y^6 25x2+10xy3+y6

STEP 6

Write the polynomial in standard form, which is already achieved as:y6+10xy3+25x2 y^6 + 10xy^3 + 25x^2 y6+10xy3+25x2The polynomial in standard form is:y6+10xy3+25x2 \boxed{y^6 + 10xy^3 + 25x^2} y6+10xy3+25x2​

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QuestionQuestion Watcl
Expand and state your answer as a polynomial in standard form. $\left(5 x+y^{3}\right)^{2}$
Answer Attempt 1 out of 2

1. We need to expand the expression $(5x + y^3)^2$ .
2. The expansion will use the formula for the square of a binomial.
3. The result should be expressed as a polynomial in standard form.

1. Apply the formula for the square of a binomial.
2. Simplify the expanded terms.
3. Write the polynomial in standard form.

Calculate each term in the expansion:
1. $(5x)^2 = 25x^2$
2. $2(5x)(y^3) = 10xy^3$
3. $(y^3)^2 = y^6$

Combine the terms to form the expanded polynomial:
$25x^2 + 10xy^3 + y^6$

Write the polynomial in standard form, which is already achieved as:
$y^6 + 10xy^3 + 25x^2$
The polynomial in standard form is:
$\boxed{y^6 + 10xy^3 + 25x^2}$