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Choose the correct simplification of [tex]7x^2(6x + 3x^2 − 4)[/tex].

A. [tex]21x^4 − 42x^3 + 28x^2[/tex]
B. [tex]42x^4 + 21x^3 − 3x^2[/tex]
C. [tex]21x^4 + 42x^3 − 28x^2[/tex]
D. [tex]42x^4 − 13x^3 + 11x^2[/tex]

Answer :

Answer:

Option (3) is correct.

[tex]7x^2(6x+3x^2-4)=21x^4+42x^3-28x^2[/tex]

Step-by-step explanation:

Given: expression [tex]7x^2(6x+3x^2-4)[/tex]

We have to write the correct simplification of the given expression [tex]7x^2(6x+3x^2-4)[/tex]

Consider the given expression [tex]7x^2(6x+3x^2-4)[/tex]

Multiply [tex]7x^2[/tex] with each term in brackets [tex](6x+3x^2-4)[/tex]

we get,

[tex]=7x^2\cdot \:6x+7x^2\cdot \:3x^2+7x^2\left(-4\right)[/tex]

Apply exponent rule, [tex]a^b\cdot \:a^c=a^{b+c}[/tex] and Simplify by multiply, we get,

[tex]=42x^3+21x^4-28x^2[/tex]

Thus, Rearranging in standard form, we get,

[tex]=21x^4+42x^3-28x^2[/tex]

Thus, Option (3) is correct.

Thanks for taking the time to read Choose the correct simplification of tex 7x 2 6x 3x 2 4 tex A tex 21x 4 42x 3 28x 2 tex B tex 42x. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

7x²(6x + 3x² - 4)

7x² × 6x = 42x³

7x² × 3x² = 21x⁴

7x² × -4 = -28x²

42x³ + 21x⁴ - 28x² is the correct answer.