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Answer :
Sure! Let's simplify the expression step-by-step:
Given expression:
[tex]\[ 2 x^3 \left( 5 x^3 - 7 \right) \][/tex]
To simplify, we use the distributive property, which says [tex]\( a(b + c) = ab + ac \)[/tex]. So, we need to distribute [tex]\( 2 x^3 \)[/tex] to both terms inside the parentheses.
Step 1: Distribute [tex]\( 2 x^3 \)[/tex] to [tex]\( 5 x^3 \)[/tex]:
[tex]\[ 2 x^3 \cdot 5 x^3 \][/tex]
When multiplying these terms, multiply the coefficients (2 and 5) and then add the exponents of [tex]\( x \)[/tex]:
[tex]\[ 2 \cdot 5 = 10 \][/tex]
[tex]\[ x^3 \cdot x^3 = x^{3+3} = x^6 \][/tex]
So,
[tex]\[ 2 x^3 \cdot 5 x^3 = 10 x^6 \][/tex]
Step 2: Distribute [tex]\( 2 x^3 \)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[ 2 x^3 \cdot (-7) \][/tex]
Multiply the coefficient 2 with -7:
[tex]\[ 2 \cdot (-7) = -14 \][/tex]
The [tex]\( x^3 \)[/tex] remains:
[tex]\[ 2 x^3 \cdot (-7) = -14 x^3 \][/tex]
Step 3: Combine the results from steps 1 and 2:
[tex]\[ 10 x^6 - 14 x^3 \][/tex]
So, the simplified expression is:
[tex]\[ 10 x^6 - 14 x^3 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{10 x^6 - 14 x^3} \][/tex]
This corresponds to option B in the list of given choices.
Given expression:
[tex]\[ 2 x^3 \left( 5 x^3 - 7 \right) \][/tex]
To simplify, we use the distributive property, which says [tex]\( a(b + c) = ab + ac \)[/tex]. So, we need to distribute [tex]\( 2 x^3 \)[/tex] to both terms inside the parentheses.
Step 1: Distribute [tex]\( 2 x^3 \)[/tex] to [tex]\( 5 x^3 \)[/tex]:
[tex]\[ 2 x^3 \cdot 5 x^3 \][/tex]
When multiplying these terms, multiply the coefficients (2 and 5) and then add the exponents of [tex]\( x \)[/tex]:
[tex]\[ 2 \cdot 5 = 10 \][/tex]
[tex]\[ x^3 \cdot x^3 = x^{3+3} = x^6 \][/tex]
So,
[tex]\[ 2 x^3 \cdot 5 x^3 = 10 x^6 \][/tex]
Step 2: Distribute [tex]\( 2 x^3 \)[/tex] to [tex]\(-7\)[/tex]:
[tex]\[ 2 x^3 \cdot (-7) \][/tex]
Multiply the coefficient 2 with -7:
[tex]\[ 2 \cdot (-7) = -14 \][/tex]
The [tex]\( x^3 \)[/tex] remains:
[tex]\[ 2 x^3 \cdot (-7) = -14 x^3 \][/tex]
Step 3: Combine the results from steps 1 and 2:
[tex]\[ 10 x^6 - 14 x^3 \][/tex]
So, the simplified expression is:
[tex]\[ 10 x^6 - 14 x^3 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{10 x^6 - 14 x^3} \][/tex]
This corresponds to option B in the list of given choices.
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