Answer:
1. 4[tex]x^{3}[/tex] + 26x² + 4x - 48
2. 2[tex]x^{3}[/tex] - 23x² + 60x - 32
3. [tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8
4. 2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12
Step-by-step explanation:
To multiply polynomials, simply distribute whatever's outside the largest set of parenthesis, then combine like terms.
1) Distribute the parenthesis (x + 6):
x(4x² + 2x - 8) + 6(4x² + 2x - 8)
4[tex]x^{3}[/tex] + 2x² -8x + 6(4x² + 2x -8)
4[tex]x^{3}[/tex] + 2x² -8x + 24x² + 12x - 48
Combine like terms:
4[tex]x^{3}[/tex] + 26x² + 4x - 48
2) Distribute the parenthesis (x - 8):
x(2x² - 7x + 4) + (-8)(2x² - 7x + 4)
2[tex]x^{3}[/tex] - 7x² + 4x + (-8)(2x² - 7x + 4)
2[tex]x^{3}[/tex] - 7x² + 4x + -16x² + 56x - 32
Combine like terms:
2[tex]x^{3}[/tex] - 23x² + 60x - 32
3) Distribute the parenthesis (x + 2):
x([tex]x^{4}[/tex] + 7x² - 4) + 2([tex]x^{4}[/tex] + 7x² - 4)
[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2([tex]x^{4}[/tex] + 7x² - 4)
[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8
No like terms to combine, so:
[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8
4) Distribute the parenthesis (x + 4):
x(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3) + 4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)
2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x + 4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)
2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x + 8 [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 12
Combine like terms:
2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12
hope this helps!
