Question

Find the product of binomial and trinomial. Show your solution. Solve the following special product using the steps of the product of binomial and trinomial.

1. (3m+7)(9m²- 21m+49)

2. (x²-2x)(x⁴-2x³+4x²)

3. (2y²-7y)(4y⁴+ 14y³+49y²)​

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Answer 1

As per questions,

1)

(3m+7)(9m²- 21m+49)

Expanding to a³±b³ formula,

→ 3m³ + 7³

→ 3³×m³ + 7³

→ 27m³ + 343

2)

(x²-2x)(x⁴-2x³+4x²)

→ x²(x⁴-2x³+4x²)-2x(x⁴-2x³+4x²)

→ x²x⁴-2x²x³+4x²x²-2x×x⁴+2x×2x³-8x×x²

→ x⁶-2x⁵+4x⁴-2x⁵+4x⁴-8x³

3)

(2y²-7y)(4y⁴+ 14y³+49y²)

→ 2y²×4y⁴ + 2y²×14y³ + 2y²×49y² -7y×14y³ -7y×49y²

→ 8y⁶+28y⁵+98y⁴-28y⁵-98y⁴

As ${y}^{a} \times {y}^{b} = {y}^{a + b}$

→ 8y⁶-343y³