(5x+4)(2x-1) (3p+2c)(2p+4c) (b-2)(b во второй степени+2b-3)

Let’s expand each expression step by step.

1. For the first expression: \( (5x + 4)(2x - 1) \)

Using the distributive property (FOIL method), we get: \[ 5x \cdot 2x + 5x \cdot (-1) + 4 \cdot 2x + 4 \cdot (-1) \] Calculating each term: \[ = 10x^2 - 5x + 8x - 4 \] Now combine like terms: \[ = 10x^2 + 3x - 4 \]

2. For the second expression: \( (3p + 2c)(2p + 4c) \)

Again using the distributive property: \[ 3p \cdot 2p + 3p \cdot 4c + 2c \cdot 2p + 2c \cdot 4c \] Calculating each term: \[ = 6p^2 + 12pc + 4pc + 8c^2 \] Now combine like terms: \[ = 6p^2 + 16pc + 8c^2 \]

3. For the third expression: \( (b - 2)(b^2 + 2b - 3) \)

Once more, using the distributive property: \[ b \cdot b^2 + b \cdot 2b + b \cdot (-3) - 2 \cdot b^2 - 2 \cdot 2b - 2 \cdot (-3) \] Calculating each term: \[ = b^3 + 2b^2 - 3b - 2b^2 - 4b + 6 \] Now combine like terms: \[ = b^3 + (2b^2 - 2b^2) + (-3b - 4b) + 6 \] This simplifies to: \[ = b^3 - 7b + 6 \]

In summary, the final results of the expansions are:

1. \( 10x^2 + 3x - 4 \)
2. \( 6p^2 + 16pc + 8c^2 \)
3. \( b^3 - 7b + 6 \)