Question

Please help me with these questions , thank you​

Answer 1

Answer:

1. 4$x^{3}$ + 26x² + 4x - 48

2. 2$x^{3}$ - 23x² + 60x - 32

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

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

4$x^{3}$ + 2x² -8x  +  6(4x² + 2x -8)

4$x^{3}$ + 2x² -8x + 24x² + 12x - 48

Combine like terms:

4$x^{3}$ + 26x² + 4x - 48

2) Distribute the parenthesis (x - 8):

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

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

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

Combine like terms:

2$x^{3}$ - 23x² + 60x - 32

3) Distribute the parenthesis (x + 2):

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

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

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

No like terms to combine, so:

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

4) Distribute the parenthesis (x + 4):

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

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

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

Combine like terms:

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

hope this helps!