Question

# Multiply: x^{2} - 8x + 8 by 6x^{2} -3x + 4

## The correct answer is: 6x4 - 51x3 + 76x2 - 56x + 32

### Answer:

- Multiplication of polynomials.

○ Follow three steps while multiplication of polynomials.

First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.

Add the powers of the same variables using the exponent rule.

Then, simplify the resulting polynomial by adding or subtracting the like term

- Step by step explanation:

○ Given:

x^{2} - 8x + 8 and 6x^{2} -3x + 4

○ Step 1:

○ multiplication

(x^{2} - 8x + 8) (6x^{2} -3x + 4)

x^{2} (6x^{2} -3x + 4) - 8x (6x^{2} -3x + 4) + 8(6x^{2} -3x + 4)

(6x^{4}-3x^{3} + 4x^{2}) - (48x^{3} -24x^{2} + 32x) + (48x^{2} -24x + 32)

(6x^{4}-3x^{3} + 4x^{2}) - (48x^{3} -24x^{2} + 32x) + (48x^{2} -24x + 32)

○ Step 2:

○ Arrange like terms in decreasing order of power

6x^{4}- 3x^{3} + 4x^{2} - 48x^{3} + 24x^{2} - 32x + 48x^{2} -24x + 32

(6x^{4}) - (48x^{3} + 3x^{3}) + (48x^{2} + 4x^{2}+ 24x^{2}) -(24x + 32x) + 32

(6x^{4}) - (51x^{3}) + (76x^{2}) - (56x) + 32

6x^{4} - 51x^{3} + 76x^{2} - 56x + 32

- Final Answer:

6x^{4} - 51x^{3} + 76x^{2} - 56x + 32

^{2}- 8x + 8) (6x

^{2}-3x + 4)

^{2}(6x

^{2}-3x + 4) - 8x (6x

^{2}-3x + 4) + 8(6x

^{2}-3x + 4)

^{4}-3x

^{3}+ 4x

^{2}) - (48x

^{3}-24x

^{2}+ 32x) + (48x

^{2}-24x + 32)

^{4}-3x

^{3}+ 4x

^{2}) - (48x

^{3}-24x

^{2}+ 32x) + (48x

^{2}-24x + 32)

○ Step 2:

○ Arrange like terms in decreasing order of power

^{4}- 3x

^{3}+ 4x

^{2}- 48x

^{3}+ 24x

^{2}- 32x + 48x

^{2}-24x + 32

^{4}) - (48x

^{3}+ 3x

^{3}) + (48x

^{2}+ 4x

^{2}+ 24x

^{2}) -(24x + 32x) + 32

^{4}) - (51x

^{3}) + (76x

^{2}) - (56x) + 32

^{4}- 51x

^{3}+ 76x

^{2}- 56x + 32

^{4}- 51x

^{3}+ 76x

^{2}- 56x + 32

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