Answer :
Let's simplify the expression [tex]\(-4x^2(3x - 7)\)[/tex] step-by-step:
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- First term: [tex]\(-4x^2 \times 3x\)[/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex]. Then, multiply the exponents of [tex]\(x\)[/tex] (i.e., [tex]\(x^2 \times x\)[/tex], which equals [tex]\(x^{2+1} = x^3\)[/tex]).
So, [tex]\(-4x^2 \times 3x = -12x^3\)[/tex].
- Second term: [tex]\(-4x^2 \times -7\)[/tex]
Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. Since there's no [tex]\(x\)[/tex] in [tex]\(-7\)[/tex], multiply with the remaining [tex]\(x^2\)[/tex].
So, [tex]\(-4x^2 \times -7 = 28x^2\)[/tex].
2. Combine the results:
The expression becomes [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
C. [tex]\(-12x^3 - 28x^2\)[/tex]
1. Distribute [tex]\(-4x^2\)[/tex] to each term inside the parentheses:
- First term: [tex]\(-4x^2 \times 3x\)[/tex]
Multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(3\)[/tex] to get [tex]\(-12\)[/tex]. Then, multiply the exponents of [tex]\(x\)[/tex] (i.e., [tex]\(x^2 \times x\)[/tex], which equals [tex]\(x^{2+1} = x^3\)[/tex]).
So, [tex]\(-4x^2 \times 3x = -12x^3\)[/tex].
- Second term: [tex]\(-4x^2 \times -7\)[/tex]
Here, multiply the coefficients [tex]\(-4\)[/tex] and [tex]\(-7\)[/tex] to get [tex]\(28\)[/tex]. Since there's no [tex]\(x\)[/tex] in [tex]\(-7\)[/tex], multiply with the remaining [tex]\(x^2\)[/tex].
So, [tex]\(-4x^2 \times -7 = 28x^2\)[/tex].
2. Combine the results:
The expression becomes [tex]\(-12x^3 + 28x^2\)[/tex].
Therefore, the simplified expression is [tex]\(-12x^3 + 28x^2\)[/tex].
The correct answer is:
C. [tex]\(-12x^3 - 28x^2\)[/tex]
