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nexus9112 [7]
2 years ago
11

Please help me with these questions , thank you​

Mathematics
1 answer:
Angelina_Jolie [31]2 years ago
8 0

Answer:

1. 4x^{3} + 26x² + 4x - 48

2. 2x^{3} - 23x² + 60x - 32

3. x^{5} + 7x^{3} - 4x + 2x^{4} + 14x² - 8

4. 2x^{7} + x^{6} - 28x^{5} + 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)

4x^{3} + 2x² -8x  +  6(4x² + 2x -8)

4x^{3} + 2x² -8x + 24x² + 12x - 48

Combine like terms:

4x^{3} + 26x² + 4x - 48

2) Distribute the parenthesis (x - 8):

x(2x² - 7x + 4)  +  (-8)(2x² - 7x + 4)

2x^{3} - 7x² + 4x  +  (-8)(2x² - 7x + 4)

2x^{3} - 7x² + 4x  +  -16x² + 56x - 32

Combine like terms:

2x^{3} - 23x² + 60x - 32

3) Distribute the parenthesis (x + 2):

x(x^{4} + 7x² - 4)  +  2(x^{4} + 7x² - 4)

x^{5} + 7x^{3} - 4x  +  2(x^{4} + 7x² - 4)

x^{5} + 7x^{3} - 4x + 2x^{4} + 14x² - 8

No like terms to combine, so:

x^{5} + 7x^{3} - 4x + 2x^{4} + 14x² - 8

4) Distribute the parenthesis (x + 4):

x(2x^{6} - 7x^{5} + 3)  +  4(2x^{6} - 7x^{5} + 3)

2x^{7} - 7x^{6} + 3x  +  4(2x^{6} - 7x^{5} + 3)

2x^{7} - 7x^{6} + 3x + 8  x^{6} - 28x^{5} + 12

Combine like terms:

2x^{7} + x^{6} - 28x^{5} + 3x + 12

hope this helps!

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