Polynomial Operations

Front

(2x+3)²

Back

4x²+12x+9

Answer explanation

To find the product of (2x+3)², use the formula (a+b)² = a² + 2ab + b². Here, a = 2x and b = 3. Thus, (2x)² = 4x², 2(2x)(3) = 12x, and 3² = 9. Combining these gives 4x² + 12x + 9, which is the correct answer.

Front

Find the sum: (3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

Back

3y³ + 7y² - 4y + 3

Answer explanation

To find the sum, combine like terms: (3y^2 + 4y^2) + (y^3 + 2y^3) + (-4y) + (-5 + 8) = 7y^2 + 3y^3 - 4y + 3. Thus, the correct answer is 3y^3 + 7y^2 - 4y + 3.

Front

Find the difference: (3 - 2x + 2x²) - (4x - 5 + 3x²)

Back

-x² - 6x + 8

Answer explanation

To find the difference, distribute the negative sign: (3 - 2x + 2x²) - (4x - 5 + 3x²) = 3 - 2x + 2x² - 4x + 5 - 3x² = -x² - 6x + 8. Thus, the correct answer is -x² - 6x + 8.

Front

Simplify the expression: -3x²( 7x² - x + 4)

Back

-21x⁴ + 3x³ -12x²

Answer explanation

To simplify -3x²(7x² - x + 4), distribute -3x² to each term: -3x² * 7x² = -21x⁴, -3x² * -x = 3x³, -3x² * 4 = -12x². Combining these gives -21x⁴ + 3x³ - 12x², which matches the correct answer.

Front

Multiply.
(b+3)(b²+2b+1)

Back

b³+5b²+7b+3

Answer explanation

To multiply (b+3)(b^2+2b+1), use the distributive property: b(b^2+2b+1) + 3(b^2+2b+1). This results in b^3 + 2b^2 + b + 3b^2 + 6b + 3, which simplifies to b^3 + 5b^2 + 7b + 3, the correct answer.

Front

(5x⁴ - 4x³ - 2x² + x - 19) - (x⁴ + 5x³ + 8x² + x + 5)

Back

4x⁴ - 9x³ - 10x² - 24

Answer explanation

To solve the expression, distribute the negative sign and combine like terms. The result simplifies to 4x^4 - 9x^3 - 10x^2 - 24, matching the first answer choice.

Front

Perimeter of rectangle: 6x^3 - 9x^2 + 10x - 15, 6x^2 + 1x - 15, 6x^2 + 4x + 4, 6x^3 + 1x^2 - 15x

Back

6x^2 + 4x + 4

Answer explanation

The perimeter of a rectangle is calculated as P = 2(length + width). Given the correct choice, 6x² + 4x + 4 represents the sum of the dimensions multiplied by 2, making it the valid perimeter expression.

Front

(2x + 3)(x² + 4x + 1)

Back

2x³ + 11x² + 14x + 3

Answer explanation

To expand (2x + 3)(x^2 + 4x + 1), use the distributive property: 2x*x^2 + 2x*4x + 2x*1 + 3*x^2 + 3*4x + 3*1. This results in 2x^3 + 8x^2 + 2x + 3x^2 + 12x + 3, which simplifies to 2x^3 + 11x^2 + 14x + 3.

Front

Subtract the polynomials: (3x³ + 3x² + 5) – (x³ – 2x² + x – 4)

Back

2x³ + 5x² – x + 9

Answer explanation

To subtract the polynomials, distribute the negative sign: (3x^3 + 3x^2 + 5) - (x^3 - 2x^2 + x - 4) = 3x^3 - x^3 + 3x^2 + 2x^2 - x + 5 + 4 = 2x^3 + 5x^2 - x + 9. Thus, the correct answer is 2x^3 + 5x^2 - x + 9.

Front

(4x+1)(5x−2)

Back

20x² − 3x − 2

Answer explanation

To expand (4x+1)(5x−2), use the distributive property: 4x*5x + 4x*(-2) + 1*5x + 1*(-2) = 20x^2 - 8x + 5x - 2 = 20x^2 - 3x - 2. Thus, the correct answer is 20x² − 3x − 2.