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
- (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:
[tex]\mathbf{4x(4x^2-x+3)}[/tex]
By using distributive law m(a+b+c) = ma + mb + mc
[tex]\mathbf{=4x(4x^2)+4x(-x)+4x(3))}[/tex]
= 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; [tex]\mathbf{a^b*a^c = a^{b+c}}[/tex]
[tex]\mathbf{= 4x^2 (4x)= x^2*4^{1+1}x}[/tex]
[tex]\mathbf{= x^2*4^{2}x}[/tex]
[tex]\mathbf{= 4^{2}x^{2+1}}[/tex]
[tex]\mathbf{= 4^{2}x^{3}}[/tex]
[tex]\mathbf{= 16x^{3}}[/tex]
(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:
https://brainly.com/question/2833285
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