Question

pre - algebra #10
practice: multiply to simplify.
1.) $3(4x) =$
2.) $-5(6a) =$
3.) $(-3)(-2n) =$
4.) $(-3n)(2) =$
5.) $(-2x)(5y) =$
6.) $(-3a)(4b) =$
7.) $-3(7xy) =$
8.) $4(-4ab) =$
9.) $-2(-6rs) =$
10.) $(8xy)(8) =$
11.) $(3bc)(-9d)$
12.) $(-3z)(-2y) =$
13.) $-5(-3a)(-2b) =$
14.) $(3b)(2c)(-4d) =$

Explanation:

Step1: Solve \(3(4x)\)

Using the distributive property \(a(bc)=(ab)c\), multiply 3 and 4 first. \(3\times4 = 12\), so \(3(4x)=12x\).

Step2: Solve \(-5(6a)\)

Multiply -5 and 6. \(-5\times6=-30\), so \(-5(6a)=-30a\).

Step3: Solve \((-3)(-2n)\)

Multiply -3 and -2. \((-3)\times(-2) = 6\), so \((-3)(-2n)=6n\).

Step4: Solve \((-3n)(2)\)

Multiply -3 and 2. \(-3\times2=-6\), so \((-3n)(2)=-6n\).

Step5: Solve \((-2x)(5y)\)

Multiply -2 and 5, and keep the variables. \((-2)\times5=-10\), so \((-2x)(5y)=-10xy\).

Step6: Solve \((-3a)(4b)\)

Multiply -3 and 4, and keep the variables. \(-3\times4=-12\), so \((-3a)(4b)=-12ab\).

Step7: Solve \(-3(7xy)\)

Multiply -3 and 7. \(-3\times7=-21\), so \(-3(7xy)=-21xy\).

Step8: Solve \(4(-4ab)\)

Multiply 4 and -4. \(4\times(-4)=-16\), so \(4(-4ab)=-16ab\).

Step9: Solve \(-2(-6rs)\)

Multiply -2 and -6. \((-2)\times(-6)=12\), so \(-2(-6rs)=12rs\).

Step10: Solve \((8xy)(8)\)

Multiply 8 and 8. \(8\times8 = 64\), so \((8xy)(8)=64xy\).

Step11: Solve \((3bc)(-9d)\)

Multiply 3 and -9, and keep the variables. \(3\times(-9)=-27\), so \((3bc)(-9d)=-27bcd\).

Step12: Solve \((-3z)(-2y)\)

Multiply -3 and -2. \((-3)\times(-2)=6\), so \((-3z)(-2y)=6zy\) (or \(6yz\)).

Step13: Solve \(-5(-3a)(-2b)\)

First multiply -5 and -3: \(-5\times(-3)=15\). Then multiply 15 and -2: \(15\times(-2)=-30\). So \(-5(-3a)(-2b)=-30ab\).

Step14: Solve \((3b)(2c)(-4d)\)

First multiply 3 and 2: \(3\times2 = 6\). Then multiply 6 and -4: \(6\times(-4)=-24\). Keep the variables, so \((3b)(2c)(-4d)=-24bcd\).

Answer:

1. \(12x\)
2. \(-30a\)
3. \(6n\)
4. \(-6n\)
5. \(-10xy\)
6. \(-12ab\)
7. \(-21xy\)
8. \(-16ab\)
9. \(12rs\)
10. \(64xy\)
11. \(-27bcd\)
12. \(6zy\) (or \(6yz\))
13. \(-30ab\)
14. \(-24bcd\)