**Question 1: ***Multiply:*

(5*x* + 3) by (7*x* + 2)

**Answer 1: To multiply, we will use distributive law as follows:**

(5x+3)(7x+2)=5x(7x+2)+3(7x+2)=(5x×7x+5x×2)+(3×7x+3×2)=(35x2+10x)+(21x+6)=35x2+10x+21x+6=35x2+31x+6Thus, the answer is 35x2+31x+635x2+31x+6.

**Question 2: ***Multiply:*

(2*x* + 8) by (*x* − 3)

**Answer 2: **To multiply the expressions, we will use the distributive law in the following way:

(2x+8)(x−3)=2x(x−3)+8(x−3)=(2x×x−2x×3)+(8x−8×3)=(2x2−6x)+(8x−24)=2x2−6x+8x−24=2x2+2x−242x+8x-3=2xx-3+8x-3=2x×x-2x×3+8x-8×3=2x2-6x+8x-24=2x2-6x+8x-24=2x2+2x-2Thus, the answer is 2x2+2x−242x2+2x-24.

**Question 3: ***Multiply:*

(7*x* + *y*) by (*x* + 5*y*)

**Answer 3: To multiply, we will use distributive law as follows:**

(7x+y)(x+5y)=7x(x+5y)+y(x+5y)=7x2+35xy+xy+5y2=7x2+36xy+5y27x+yx+5y=7xx+5y+yx+5y=7x2+35xy+xy+5y2=7x2+36xy+5y2

Thus, the answer is 7x2+36xy+5y27x2+36xy+5y2.

**Question 4: ***Multiply:*

(*a* − 1) by (0.1*a*^{2} + 3)

**Answer 4: To multiply, we will use distributive law as follows:**

(a−1)(0.1a2+3)=0.1a2(a−1)+3(a−1)=0.1a3−0.1a2+3a−3a-10.1a2+3=0.1a2a-1+3a-1=0.1a3-0.1a2+3a-3

Thus, the answer is 0.1a3−0.1a2+3a−30.1a3-0.1a2+3a-3.

**Question 5: ***Multiply:*

(3*x*^{2} + *y*^{2}) by (2*x*^{2} + 3*y*^{2})

**Answer 5: ****To multiply, we will use distributive law as follows:**

(3x2+y2)(2x2+3y2)=3x2(2x2+3y2)+y2(2x2+3y2)=6x4+9x2y2+2x2y2+3y4=6x4+11x2y2+3y43x2+y22x2+3y2=3x22x2+3y2+y22x2+3y2=6x4+9x2y2+2x2y2+3y4=6x4+11x2y2+3yThus, the answer is 6x4+11x2y2+3y46x4+11x2y2+3y4.

**Question 6: ***Multiply:*

**Answer 6: To multiply, we will use distributive law as follows: **

**Thus, the answer is **

**Question 7: ***Multiply:*

(*x*^{6} − *y*^{6}) by (*x*^{2}^{ }+ *y*^{2})

**Answer 7: To multiply, we will use distributive law as follows: **

**(x6−y6)(x2+y2)=x6(x2+y2)−y6(x2+y2)=(x8+x6y2)−(y6x2+y8)=x8+x6y2−y6x2−y8 Thus, the answer is x8+x6y2−y6x2−y8x8+x6y2-y6x2-y8. **

**Question 8: ***Multiply:*

(*x*^{2} + *y*^{2}) by (3*a* + 2*b*)

**Answer 8: To multiply, we will use distributive law as follows: **

**(x2+y2)(3a+2b)=x2(3a+2b)+y2(3a+2b)=3ax2+2bx2+3ay2+2by2 Thus, the answer is 3ax2+2bx2+3ay2+2by23ax2+2bx2+3ay2+2by2. **

**Question 9: ***Multiply:*

[−3*d* + (−7*f*)] by (5*d* + *f*)

**Answer 9: To multiply, we will use distributive law as follows:**

[−3d+(−7f)](5d+f)=(−3d)(5d+f)+(−7f)(5d+f)=(−15d2−3df)+(−35df−7f2)=−15d2−3df−35df−7f2=−15d2−38df−7f2Thus, the answer is −15d2−38df−7f2-15d2-38df-7f2.

**Question 10: ***Multiply:*

(0.8*a* − 0.5*b*) by (1.5*a* − 3*b*)

**Answer 10: To multiply, we will use distributive law as follows:**

(0.8a−0.5b)(1.5a−3b)=0.8a(1.5a−3b)−0.5b(1.5a−3b)=1.2a2−2.4ab−0.75ab+1.5b2=1.2a2−3.15ab+1.5b2Thus, the answer is 1.2a2−3.15ab+1.5b21.2a2-3.15ab+1.5b2.

**Question 11: ***Multiply:*

(2*x*^{2}*y*^{2} − 5*xy*^{2}) by (*x*^{2} − *y*^{2})

**Answer 11: To multiply, we will use distributive law as follows:**

**(2x2y2−5xy2)(x2−y2)=2x2y2(x2−y2)−5xy2(x2−y2)=2x4y2−2x2y4−5x3y2+5xy4 Thus, the answer is **