(×+3y)(×2+2×y-4×2)
Expanding the expression:
(×+3y)(×2+2×y-4×2)
= (××2) + (××2y) - (××4×2) + (3y×2) + (3y×2y) - (3y×4×2)
= 2×^2 + 2xy - 8x + 6y + 6xy - 24y
= 2×^2 + 8xy - 8x - 18y
Therefore, (×+3y)(×2+2×y-4×2) = 2×^2 + 8xy - 8x - 18y.
To expand the expression (×+3y)(×2+2×y-4×2), you can use the distributive property. This property states that for any three numbers a, b, and c, the expression a(b + c) is equal to ab + ac.
Applying this property to the given expression:
(× + 3y)(×2 + 2×y - 4×2)
= ×(×2 + 2×y - 4×2) + 3y(×2 + 2×y - 4×2)
Now, we can simplify each term within the brackets:
= ×(2× + 2×y - 4×2) + 3y(2× + 2×y - 4×2)
Distributing × to each term in the first bracket gives:
= 2× × + 2× × y - 4× × 2 + 3y(2× + 2×y - 4×2)
= 2×^2 + 2× × y - 4× × 2 + 3y(2× + 2×y - 4×2)
Similarly, distributing 3y to each term in the second bracket gives:
= 2×^2 + 2× × y - 4× × 2 + 2×y × 3y + 2×y × 2×y - 2×y × 4×2
Simplifying further:
= 2×^2 + 2× × y - 4× × 2 + 6yx + 4×y^2 - 16×y
Therefore, the expanded form of (×+3y)(×2+2×y-4×2) is:
2×^2 + 2× × y - 4× × 2 + 6yx + 4×y^2 - 16×y