Question

Find the product of (2x − 3)(2x2 7x − 1). 4x3 − 6x2 − 9x 3 4x3 8x2 − 23x 3 4x3 20x2 − 9x 3 4x3 − 6x2 − 23x 3.

Answer 1

Product of polynomials can be done by distribution of multiplication over addition. The product of  $(2x - 3)(2x^2 + 7x - 1)$ is $4x^3 + 8x^2 -23x + 3$

What is distributive property of multiplication over addition?

Suppose a, b and c are three numbers. Then we have:

$a(b + c) = a\times b + a\times c$

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The product result of the given expression is

$(2x - 3)(2x^2 + 7x - 1) = 2x(2x^2 + 7x - 1) -3(2x^2 + 7x - 1) \\(2x - 3)(2x^2 + 7x - 1) = 4x^{1+2} + 14x^2 -2x - 6x^2 - 21x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + (14 -6)x^2 + (-2 -21)x + 3\\(2x - 3)(2x^2 + 7x - 1) = 4x^3 + 8x^2 -23x + 3$

It is because when bases are same and there is multiplication, then powers add up, so we have: $a^b \times a^c = a^{b+c}$

Also, we've

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

where -ve, +ve are sign of operands and result.

That's why $2 \times -1 = -2$

Thus,

The product of   $(2x - 3)(2x^2 + 7x - 1)$  is $4x^3 + 8x^2 -23x + 3$

Learn more about product of polynomials here:

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