Question

1. directions

drag and drop the correct answer choice to each answer blank. or, touch the answer choice followed by the answer blank.
write an expression that is equivalent to \\(\left(x^{2}+3x - 4\
ight)\left(2x + 1\
ight)\\)
\\(x^{3}\\) \\(2x^{3}\\) \\(6x^{3}\\) \\(6x^{2}\\) \\(5x^{2}\\) \\(7x^{2}\\)
move the correct answer to each box. not all answers will be used.
\\(\square + \square - 5x - 4\\)

Explanation:

Step1: Expand the product

Use the distributive property (FOIL method for polynomials):
$$(x^2 + 3x - 4)(2x + 1)=x^2(2x + 1)+3x(2x + 1)-4(2x + 1)$$

Step2: Distribute each term

• For \(x^2(2x + 1)\): \(x^2\times2x + x^2\times1 = 2x^3+x^2\)
• For \(3x(2x + 1)\): \(3x\times2x + 3x\times1 = 6x^2+3x\)
• For \(-4(2x + 1)\): \(-4\times2x + (-4)\times1 = -8x - 4\)

Step3: Combine like terms

Combine the results from Step2:

$$
LATEXBLOCK0
$$

Answer:

The first blank (the cubic term) is \(2x^3\) and the second blank (the quadratic term) is \(7x^2\). So the filled expression is \(2x^3 + 7x^2-5x - 4\), with the first box containing \(2x^3\) and the second box containing \(7x^2\).