Answer:
8 x^4 + -26 x^2 + 21
Step-by-step 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
