EXERCISE 4 Fully simplify eac 1. \( (2 x+y)\left(3 x^{2}+\right. \) 3. \( (x-y)(3 x-2 \) 5. \( (7 m-3 n)(5 m \) 7. \( (2 x-y)\left(4 x^{2}+\right. \)
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The Deep Dive
To fully simplify the given expressions, let's break them down step by step for clarity and engagement! 1. \( (2x + y)(3x^2 + 1) = 6x^3 + 2xy + 3xy + y = 6x^3 + 5xy + y \) 3. \( (x - y)(3x - 2) = 3x^2 - 2x - 3xy + 2y = 3x^2 - 3xy - 2x + 2y \) 5. \( (7m - 3n)(5m) = 35m^2 - 15mn \) 7. \( (2x - y)(4x^2 + 1) = 8x^3 + 2x - 4xy - y = 8x^3 - 4xy + 2x - y \) Each expression combines basic algebraic principles—distributing, combining like terms, and keeping things organized! If you ever find yourself stuck, just remember to take it step by step, and don’t hesitate to treat it like a mini math adventure!