Question

Match the multiplication problem on the left with the simplified polynomial on the right.

Answer 1

The match of the multiplication problem with the simplified expressions is as follows:

• 4x(4x²-x+3) ⇒ 16x³ - 4x² + 12x

• (8x + 1)(2x -3) ⇒ 16x² - 22x - 3

• 4x² (4x) ⇒ 16x³

• (2x + 3) (8x² - 4x + 3) ⇒ 16x³ + 16x² - 6x + 9

Multiplication of polynomial expressions.

The process involved in multiplying polynomial expression requires using all the parameters in parentheses to multiply each other.

From the given information:

$\mathbf{4x(4x^2-x+3)}$

By using distributive law m(a+b+c) = ma + mb + mc

$\mathbf{=4x(4x^2)+4x(-x)+4x(3))}$

= 16x³ - 4x² + 12x

(8x + 1)(2x -3)

By applying FOIL method: (a+b)(c+d) = ac + ad + bc + bd

= (8x (2x)) + (8x(-3)) + (1 × 2x) + (1 × (-3))

= 16x² - 22x - 3

4x² (4x)

Applying exponent rule; $\mathbf{a^b*a^c = a^{b+c}}$

$\mathbf{= 4x^2 (4x)= x^2*4^{1+1}x}$

$\mathbf{= x^2*4^{2}x}$

$\mathbf{= 4^{2}x^{2+1}}$

$\mathbf{= 4^{2}x^{3}}$

$\mathbf{= 16x^{3}}$

(2x + 3) (8x² - 4x + 3)

Using distributive parentheses:

= 2x(8x² - 4x + 3) + 3(8x² - 4x + 3)

= 16x³ + 16x² - 6x + 9

Learn more about polynomial expressions here:

brainly.com/question/2833285

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