Solved on Feb 27, 2024

Distribute $3 x(x-7)$ and select the simplified answer.

STEP 1

Assumptions
1. We are given the algebraic expression $3x(x-7)$ .
2. We need to apply the distributive property to simplify the expression.

STEP 2

Apply the distributive property, which states that $a(b+c) = ab + ac$ for any real numbers $a$ , $b$ , and $c$ .

STEP 3

In our case, $a = 3x$ , $b = x$ , and $c = -7$ . Now distribute $3x$ to both $x$ and $-7$ .
$3x(x-7) = 3x \cdot x + 3x \cdot (-7)$

STEP 4

Multiply $3x$ by $x$ to get the first term of the simplified expression.
$3x \cdot x = 3x^2$

STEP 5

Multiply $3x$ by $-7$ to get the second term of the simplified expression.
$3x \cdot (-7) = -21x$

STEP 6

Combine the results from STEP_4 and STEP_5 to write the simplified expression.
$3x^2 - 21x$

STEP 7

Match the simplified expression with the correct answer from the given options.
The simplified expression is $3x^2 - 21x$ , which corresponds to option D.
The correct answer is: $3 x^{2}-21 x$

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Distribute $3 x(x-7)$ and select the simplified answer.

STEP 1

Assumptions
1. We are given the algebraic expression $3x(x-7)$ .
2. We need to apply the distributive property to simplify the expression.

STEP 2

Apply the distributive property, which states that $a(b+c) = ab + ac$ for any real numbers $a$ , $b$ , and $c$ .

STEP 3

In our case, $a = 3x$ , $b = x$ , and $c = -7$ . Now distribute $3x$ to both $x$ and $-7$ .
$3x(x-7) = 3x \cdot x + 3x \cdot (-7)$

STEP 4

Multiply $3x$ by $x$ to get the first term of the simplified expression.
$3x \cdot x = 3x^2$

STEP 5

Multiply $3x$ by $-7$ to get the second term of the simplified expression.
$3x \cdot (-7) = -21x$

STEP 6

Combine the results from STEP_4 and STEP_5 to write the simplified expression.
$3x^2 - 21x$

STEP 7

Match the simplified expression with the correct answer from the given options.
The simplified expression is $3x^2 - 21x$ , which corresponds to option D.
The correct answer is: $3 x^{2}-21 x$

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Distribute 3x(x−7)3 x(x-7)3x(x−7) and select the simplified answer.

STEP 1

Assumptions1. We are given the algebraic expression 3x(x−7)3x(x-7)3x(x−7).2. We need to apply the distributive property to simplify the expression.

STEP 2

Apply the distributive property, which states that a(b+c)=ab+aca(b+c) = ab + aca(b+c)=ab+ac for any real numbers aaa, bbb, and ccc.

STEP 3

In our case, a=3xa = 3xa=3x, b=xb = xb=x, and c=−7c = -7c=−7. Now distribute 3x3x3x to both xxx and −7-7−7.3x(x−7)=3x⋅x+3x⋅(−7)3x(x-7) = 3x \cdot x + 3x \cdot (-7)3x(x−7)=3x⋅x+3x⋅(−7)

STEP 4

Multiply 3x3x3x by xxx to get the first term of the simplified expression.3x⋅x=3x23x \cdot x = 3x^23x⋅x=3x2

STEP 5

Multiply 3x3x3x by −7-7−7 to get the second term of the simplified expression.3x⋅(−7)=−21x3x \cdot (-7) = -21x3x⋅(−7)=−21x

STEP 6

Combine the results from STEP_4 and STEP_5 to write the simplified expression.3x2−21x3x^2 - 21x3x2−21x

STEP 7

Match the simplified expression with the correct answer from the given options.The simplified expression is 3x2−21x3x^2 - 21x3x2−21x, which corresponds to option D.The correct answer is: 3x2−21x3 x^{2}-21 x3x2−21x

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

Distribute $3 x(x-7)$ and select the simplified answer.

Assumptions
1. We are given the algebraic expression $3x(x-7)$ .
2. We need to apply the distributive property to simplify the expression.

Apply the distributive property, which states that $a(b+c) = ab + ac$ for any real numbers $a$ , $b$ , and $c$ .

In our case, $a = 3x$ , $b = x$ , and $c = -7$ . Now distribute $3x$ to both $x$ and $-7$ .
$3x(x-7) = 3x \cdot x + 3x \cdot (-7)$

Multiply $3x$ by $x$ to get the first term of the simplified expression.
$3x \cdot x = 3x^2$

Multiply $3x$ by $-7$ to get the second term of the simplified expression.
$3x \cdot (-7) = -21x$

Combine the results from STEP_4 and STEP_5 to write the simplified expression.
$3x^2 - 21x$

Match the simplified expression with the correct answer from the given options.
The simplified expression is $3x^2 - 21x$ , which corresponds to option D.
The correct answer is: $3 x^{2}-21 x$