Algebra Polynomial Multiplication and Exponents

Questions and Answers

What is the result of (11x + 11)(8x + 4)?

88x^2 + 132x + 44

What is the result of (7x + 8)(5x + 2)?

35x^2 + 54x + 16

What is the result of (7x + 11)(8x + 4)?

56x^2 + 116x + 44

What is the result of (7x + 12)(10x + 7)?

70x^2 + 169x + 84 Signup and view all the answers

What is the result of (-9x + 3)(6x - 8)?

-54x^2 + 90x - 24 Signup and view all the answers

What is the result of (-5x - 4)(-2x + 3)?

10x^2 - 7x - 12 Signup and view all the answers

What is the result of (12x + 8)(6x + 5)?

72x^2 + 108x + 40 Signup and view all the answers

What is the result of (10x + 10)(-10x + 4)?

-100x^2 - 60x + 40 Signup and view all the answers

What is the result of (-8x - 9)(-2x - 4)?

16x^2 + 50x + 36 Signup and view all the answers

What is the result of (-2x + 5)(-9x + 10)?

18x^2 - 65x + 50 Signup and view all the answers

What is the result of (12x + 16)(9x - 8)?

108x^2 + 48x - 128 Signup and view all the answers

What is the result of (10x - 6)(-18x - 17)?

-180x^2 - 62x + 102 Signup and view all the answers

What is the result of (-12x - 9)(-15x + 10)?

180x^2 + 15x - 90 Signup and view all the answers

What is the result of (-20x + 6)(16x + 17)?

-320x^2 - 244x + 102 Signup and view all the answers

What is the result of (-6x + 14)(16x - 20)?

-96x^2 + 344x - 280 Signup and view all the answers

What is the result of (-20x - 12)(7x - 12)?

-140x^2 + 156x + 144 Signup and view all the answers

What is the result of (6x + 12)(-10x + 8)?

-60x^2 - 72x + 96 Signup and view all the answers

What is the result of (-15x + 12)(-9x - 7)?

135x^2 - 3x - 84 Signup and view all the answers

What is the result of (9x - 12)(9x - 13)?

81x^2 - 225x + 156 Signup and view all the answers

What is the result of (20x - 19)(-10x - 12)?

-200x^2 - 50x + 228 Signup and view all the answers

What is the value of 3^3?

27 Signup and view all the answers

What is the value of 2^2?

4 Signup and view all the answers

What is the value of 4^0?

1 Signup and view all the answers

What is the value of 6^0?

1 Signup and view all the answers

What is the value of 6^2?

36 Signup and view all the answers

What is the value of 5^3?

125 Signup and view all the answers

What is the value of (-4)^0?

1/1 Signup and view all the answers

What is the value of (-3)^2?

9 Signup and view all the answers

What is the value of 6^-4?

1/1296 Signup and view all the answers

What is the value of (-2)^-3?

-1/8 Signup and view all the answers

What is the value of (-2)^-2?

1/4 Signup and view all the answers

What is the value of 5^-3?

1/125 Signup and view all the answers

What is the value of 0.5^-2?

4/1=4 Signup and view all the answers

What is the value of 0.07^4?

2401/100,000,000 Signup and view all the answers

What is the value of 0.09^3?

729/1,000,000 Signup and view all the answers

What is the value of 1.2^-1?

5/6 Signup and view all the answers

What is the value of (-8)^-3?

-1/512 Signup and view all the answers

What is the value of (-0.1)^2?

1/100 Signup and view all the answers

What is the value of [2/4]^3?

1/8 Signup and view all the answers

What is the value of [-2/3]^-1?

-3/2= -1 1/2 Signup and view all the answers

What is the value of 0.05^-2?

400/1 Signup and view all the answers

What is the value of [-8/12]^-3?

-27/8 = -3 3/8 Signup and view all the answers

What is the value of (-0.12)^4?

81/390625 Signup and view all the answers

What is the value of (-0.6)^-3?

-125/27 Signup and view all the answers

What is the value of [5/12]^1?

5/12 Signup and view all the answers

What is the value of 0.02^-1?

50/1= 50 Signup and view all the answers

What is the value of (-0.8)^2?

16/25 Signup and view all the answers

What is the value of [2/4]^1?

1/2 Signup and view all the answers

What is the value of (-0.09)^-2?

10,000/81 Signup and view all the answers

What is the value of [5/6]^3?

125/216 Signup and view all the answers

What is the value of [5/10]^-3?

8/1= 8 Signup and view all the answers

What is the value of (-0.09)^3?

-729/1,000,000 Signup and view all the answers

Study Notes

Polynomial Multiplication

Expressions involving binomials can be expanded using the distributive property.
For example, multiplying (11x + 11)(8x + 4) results in 88x² + 132x + 44.
Expanding (7x + 8)(5x + 2) results in a polynomial 35x² + 54x + 16.
Knowing how to multiply coefficients and add exponents is crucial for these calculations.

Special Products

When multiplying binomials with both positive and negative coefficients, such as (-9x + 3)(6x - 8), the output is -54x² + 90x - 24.
Negative signs can significantly affect the product, demonstrated by multiplying (-20x + 6)(16x + 17) yielding -320x² - 244x + 102.

Exponents and Powers

Exponents represent repeated multiplication of a base number; for example, 3³ equals 27.
Any non-zero number raised to the power of zero equals one, e.g., 4⁰ = 1 and 6⁰ = 1.
Negative exponents represent reciprocal values; for instance, 6⁻⁴ = 1/1296.

Special Cases with Negative Bases

Negative bases raised to even powers result in positive outcomes, such as (-3)² = 9.
When negative bases are raised to negative powers, the result is a negative fraction: (-2)⁻³ = -1/8.

Fractional and Decimal Exponents

Exponentiation can also be applied to fractions and decimals; for example, (2/4)³ = 1/8.
The process works similarly for decimals: 0.05⁻² equals 400.

Key Fractional Outcomes

When raising fractions to negative powers, the expression's outcome is the reciprocal of the base raised to the opposite power, like [-2/3]⁻¹ = -3/2 or -1 1/2.
Raising fractions like [5/10]⁻³ results in a whole value: 8/1 = 8.

Conclusions on Calculations

Careful execution of polynomial multiplication and exponent rules leads to accurate results essential in algebra.
Understanding these concepts lays the groundwork for more advanced algebraic expressions and computations.

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Description

This quiz covers polynomial multiplication techniques, including special products and the significance of negative coefficients. It also discusses exponents and their properties, including how to handle negative bases. Test your understanding of these vital algebra concepts.