Question

Find the product (2x^2-3)(4x^2-7)

Answer 1

`8x^(4) - 26x^(2) + 21`

Explanation:

I am assuming the equation is this:
`(2x^(2)-3)(4x^(2)-7)`.

We can the distributive property to solve this:

`(2x^(2)-3)(4x^(2)-7)\\= 8x^(4) - 14x^(2) - 12x^(2)+21\\= 8x^(4) - 26x^(2)+21`

Answer 2

8 x^4 + -26 x^2 + 21

Explanation:

Expand the following:

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

Hint: | Multiply 2 x^2 - 3 and 4 x^2 - 7 together using FOIL.

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

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

Hint: | Combine products of like terms.

2 x^2×4 x^2 = 2 x^4×4:

8 x^4 - 3 4 x^2 - 7 2 x^2 - 3 (-7)

Hint: | Multiply 2 and 4 together.

2×4 = 8:

8 x^4 - 3 4 x^2 - 7 2 x^2 - 3 (-7)

Hint: | Multiply -7 and 2 together.

-7×2 = -14:

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

Hint: | Multiply -3 and 4 together.

-3×4 = -12:

8 x^4 + -12 x^2 - 14 x^2 - 3 (-7)

Hint: | Multiply -3 and -7 together.

-3 (-7) = 21:

8 x^4 - 12 x^2 - 14 x^2 + 21

Hint: | Group like terms in 8 x^4 - 12 x^2 - 14 x^2 + 21.

Grouping like terms, 8 x^4 - 12 x^2 - 14 x^2 + 21 = 8 x^4 + (-14 x^2 - 12 x^2) + 21:

8 x^4 + (-14 x^2 - 12 x^2) + 21

Hint: | Combine like terms in -14 x^2 - 12 x^2.

-14 x^2 - 12 x^2 = -26 x^2:

Answer: 8 x^4 + -26 x^2 + 21