Question

multiply the given polynomial (m³-2m+3) (m⁴-2m²+3m+2)

Answer 1

Answer:

= m³(m⁴ – 2m² + 3m + 2) – 2m(m⁴ – 2m² + 3m + 2) + 3(m⁴ – 2m² + 3m + 2)

= m⁷ – 2m⁵ + 3m⁴ + 2m³ – 2m⁵ + 4m³ – 6m² – 4m + 3m⁴ – 6m² + 9m + 6

= m⁷ – 2m⁵ – 2m⁵ + 3m⁴ + 3m⁴ + 2m³ + 4m³ – 6m² – 6m² – 4m + 9m + 6

= m⁷ – 4m⁵ + 6m⁴ + 6m³ – 12m² + 5m + 6.

Hope it helps you

Answer 2

Answer:

The required product is m⁷ – 4m⁵ $+$ 6m⁴ $+$ 6m³ – 12m² $+$ 5m + 6.

Step-by-step explanation:

Laws of exponents:-

• $a^ma^n=a^{m+n}$
• $\frac{a^m}{a^n}=a^{m-n}$

Some sign rules:-

• $(-)\times(-)=(+)$
• $(+)\times(+)=(+)$
• $(-)\times (+)=(+)=(+)\times(-)$

Step 1 of 3

Consider the given polynomial as follows:

(m³ - 2m + 3)(m⁴ - 2m² + 3m + 2)

Open the brackets as follows:

m³(m⁴ – 2m² + 3m + 2) – 2m(m⁴ – 2m² + 3m + 2) + 3(m⁴ – 2m² + 3m + 2)

Using the laws of exponents, simplify as follows:

m⁷ – 2m⁵ + 3m⁴ + 2m³ – 2m⁵ $+$ 4m³ – 6m² – 4m + 3m⁴ – 6m² + 9m + 6

Step 2 of 3

Collect the like terms as follows:

m⁷ – 2m⁵ – 2m⁵ $+$ 3m⁴ + 3m⁴ $+$ 2m³ + 4m³ – 6m² – 6m² – 4m $+$ 9m + 6

Step 3 of 3

Now, simplify the polynomial as follows:

m⁷ – 4m⁵ + 6m⁴ $+$ 6m³ – 12m² $+$ 5m + 6

Final answer: The required product is m⁷ – 4m⁵ $+$ 6m⁴ $+$ 6m³ – 12m² + 5m $+$ 6.

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