Question

multiplying polynomials
multiply and simplify each of the following completely.
give your answers as simplified expressions written in descending order.
original expression | simplified expression
$3x(6x + 7)$ |
$3x(2x^2 + 4x + 10)$ |
$(6x + 7)(6x - 7)$ |
$(6x + 7)(2x - 10)$ |

Explanation:

Step1: Distribute $3x$ to each term

$3x \cdot 6x + 3x \cdot 7$

Step2: Calculate and simplify

$18x^2 + 21x$

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Step1: Distribute $3x$ to each term

$3x \cdot 2x^2 + 3x \cdot 4x + 3x \cdot 10$

Step2: Calculate and simplify

$6x^3 + 12x^2 + 30x$

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Step1: Use difference of squares formula

$(a+b)(a-b)=a^2-b^2$, where $a=6x, b=7$
$(6x)^2 - 7^2$

Step2: Calculate and simplify

$36x^2 - 49$

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Step1: Use FOIL method to expand

$6x \cdot 2x + 6x \cdot (-10) + 7 \cdot 2x + 7 \cdot (-10)$

Step2: Calculate each product

$12x^2 - 60x + 14x - 70$

Step3: Combine like terms

$12x^2 - 46x - 70$

Answer:

1. $18x^2 + 21x$
2. $6x^3 + 12x^2 + 30x$
3. $36x^2 - 49$
4. $12x^2 - 46x - 70$