Question

simplify the expression using distribution:

1. -6(x + 8) =
2. 4(1 + 9x) =
3. 6(-5x + 7) =
4. (9x + 10)2 =
5. -8(-3x - 4) =
6. 8(-3x - 4) =
7. 5(1 - 7x) =
8. -4(-6x + 7) =

Explanation:

Step1: Apply distributive property

For an expression \(a(b + c)=ab+ac\).

1. For \(-6(x + 8)\), we have \(-6\times x+(-6)\times8=-6x - 48\).
2. For \(4(1 + 9x)\), we have \(4\times1+4\times9x=4 + 36x\).
3. For \(6(-5x + 7)\), we have \(6\times(-5x)+6\times7=-30x + 42\).
4. For \((9x + 10)2\) (which is equivalent to \(2(9x + 10)\)), we have \(2\times9x+2\times10 = 18x+20\).
5. For \(-8(-3x - 4)\), we have \(-8\times(-3x)+(-8)\times(-4)=24x + 32\).
6. For \(8(-3x - 4)\), we have \(8\times(-3x)+8\times(-4)=-24x-32\).
7. For \(5(1 - 7x)\), we have \(5\times1+5\times(-7x)=5 - 35x\).
8. For \(-4(-6x + 7)\), we have \(-4\times(-6x)+(-4)\times7 = 24x-28\).

Answer:

1. \(-6x - 48\)
2. \(4 + 36x\)
3. \(-30x + 42\)
4. \(18x + 20\)
5. \(24x + 32\)
6. \(-24x-32\)
7. \(5 - 35x\)
8. \(24x-28\)