(b) 4. (2x+7)+7cdot (x-4)= (d) 5. (3x+4)-2cdot (3x-2)= (3x+1)cdot 4-7cdot (5x-3)= Alan a)

Let's solve each expression step by step:<br /><br />h) \(4. (2x+7)+7\cdot (x-4)\)<br /><br />First, distribute the 7 in the second term:<br />\[ 4. (2x + 7) + 7 \cdot (x - 4) = 4 \cdot (2x + 7) + 7 \cdot (x - 4) \]<br /><br />Now, distribute the 4 and the 7:<br />\[ = 4 \cdot 2x + 4 \cdot 7 + 7 \cdot x - 7 \cdot 4 \]<br />\[ = 8x + 28 + 7x - 28 \]<br /><br /> = 8x + 7x + 28 - 28 \]<br />\[ = 15x \]<br /><br />So, the simplified expression is:<br />\[ 4. (2x+7)+7\cdot (x-4) = 15x \]<br /><br />d) \(5. (3x+4)-2\cdot (3x-2)\)<br /><br />First, distribute the -2 in the second term:<br />\[ 5. (3x + 4) - 2 \cdot (3x - 2) = 5 \cdot (3x + 4) - 2 \cdot (3x - 2) \]<br /><br />Now, distribute the 5 and the -2:<br />\[ = 5 \cdot 3x + 5 \cdot 4 - 2 \cdot cdot 2 \]<br />\[ = 15x + 20 - 6x + 4 \]<br /><br />Combine like terms:<br />\[ = 15x - 6x + 20 + 4 \]<br />\[ = 9x + 24 \]<br /><br />So, the simplified expression is:<br />\[ 5. (3x+4)-2\cdot (3x-2) = 9x + 24 \]<br /><br />e) \((3x+1)\cdot 4-7\cdot (5x-3)\)<br /><br />First, distribute the 4 in the first term and the -7 in the second term:<br />\[ (3x + 1) \cdot 4 - 7 \cdot (5x - 3) = 4 \cdot (3x + 1) - 7 \cdot (5x - 3) \4 and the -7:<br />\[ = 4 \cdot 3x + 4 \cdot 1 - 7 \cdot 5x + 7 \cdot 3 \]<br />\[ = 12x + 4 - 35x + 21 \]<br /><br />Combine like terms:<br />\[ = 12x - 35x + 4 + 21 \]<br />\[ = -23x + 25 \]<br /><br />So, the simplified expression is:<br />\[ (3x+1)\cdot 4-7\cdot (5x-3) = -23x + 25 \]