Question

a) (3s + 5)(2s + 2) + (3s + 7)(s + 6)
b) (2x + 3)(5x + 4) + (x - 4)(3x - 7)

Explanation:

Let's solve part (a) and part (b) one by one.

Part (a)

We need to expand and simplify \((3s + 5)(2s + 2)+(3s + 7)(s + 6)\)

Step 1: Expand each product using the distributive property (FOIL method)

• Expand \((3s + 5)(2s + 2)\):

$$
LATEXBLOCK0
$$

• Expand \((3s + 7)(s + 6)\):

$$
LATEXBLOCK1
$$

Step 2: Add the two expanded expressions together

$$
LATEXBLOCK2
$$

Part (b)

We need to expand and simplify \((2x + 3)(5x + 4)+(x - 4)(3x - 7)\)

Step 1: Expand each product using the distributive property (FOIL method)

• Expand \((2x + 3)(5x + 4)\):

$$
LATEXBLOCK3
$$

• Expand \((x - 4)(3x - 7)\):

$$
LATEXBLOCK4
$$

Step 2: Add the two expanded expressions together

$$
LATEXBLOCK5
$$

Final Answers

a) \(\boldsymbol{9s^{2}+41s + 52}\)

b) \(\boldsymbol{13x^{2}+4x + 40}\)

Answer:

Let's solve part (a) and part (b) one by one.

Part (a)

We need to expand and simplify \((3s + 5)(2s + 2)+(3s + 7)(s + 6)\)

Step 1: Expand each product using the distributive property (FOIL method)

• Expand \((3s + 5)(2s + 2)\):

$$
LATEXBLOCK0
$$

• Expand \((3s + 7)(s + 6)\):

$$
LATEXBLOCK1
$$

Step 2: Add the two expanded expressions together

$$
LATEXBLOCK2
$$

Part (b)

We need to expand and simplify \((2x + 3)(5x + 4)+(x - 4)(3x - 7)\)

Step 1: Expand each product using the distributive property (FOIL method)

• Expand \((2x + 3)(5x + 4)\):

$$
LATEXBLOCK3
$$

• Expand \((x - 4)(3x - 7)\):

$$
LATEXBLOCK4
$$

Step 2: Add the two expanded expressions together

$$
LATEXBLOCK5
$$

Final Answers

a) \(\boldsymbol{9s^{2}+41s + 52}\)

b) \(\boldsymbol{13x^{2}+4x + 40}\)