Question

Which expression is equivalent to (x^2 - 2x)(3x^2 + 4x - 7)

Answer 1

To find an equivalent expression to
`(x^2 - 2x)(3x^2 + 4x - 7)`, the binomial is expanded and multiplied by the trinomial, resulting in the expression
`3x^4 - 2x^3 - 15x^2`+ 14x after combining like terms.

Step-by-step explanation:

Finding the Equivalent Expression

To find an expression equivalent to
`(x^2 - 2x)(3x^2 + 4x - 7)`, we need to use the distributive property to expand and multiply the binomial by the trinomial. Here are the steps for expansion:

Multiply
`x^2` by each term in the trinomial:
`x^2 * 3x^2 = 3x^4, x^2` * 4x = 4
`x^3`, and
`x^2 * -7 = -7x^2`.

Multiply -2x by each term in the trinomial: -2x * 3
`x^2` = -6
`x^3`, -2x * 4x = -8
`x^2`, and -2x * -7 = 14x.

Combine like terms from the products of the previous steps to get the final expanded expression: 3
`x^4 + (4x^3 - 6x^3) + (-7x^2 - 8x^2)` + 14x,

Simplify the terms: 3
`x^4 - 2x^3 - 15x^2` + 14x.

The equivalent expression after multiplying and combining like terms is
`3x^4 - 2x^3 - 15x^2` + 14x.

Answer 2

`3x^4-2x^3-15x^2+14x`

Step-by-step explanation:

`(x^2 - 2x)(3x^2 + 4x - 7)`

To find equivalent expression we multiply each term in first parenthesis with each term in second parenthesis

Multiply x^2 inside second parenthesis

`x^2(3x^2 + 4x - 7)= 3x^4+4x^3-7x^2`

`-2x(3x^2 + 4x - 7)=-6x^3-8x^2+14x`

now we keep all the terms together

`3x^4+4x^3-7x^2-6x^3-8x^2+14x`

Now we combine like terms

`3x^4-2x^3-15x^2+14x`