3e) $$ (a-b)(3 a+7 b) \quad(1-b)(3 a+7 b) $$ $$ =a imes 3 a \quad a imes 7 b-b imes 3 a \quad-b imes 7 b $$ $$ =3 a^{2}+7 a b-3 a b-70 $$ $$ =3 a^{2}+4 a b-7 b $$ 3f) $$ \left(3 x^{2}-7 ight)\left(12+2 x^{2} ight) \quad\left(35 x^{2}-7 ight)\left(12+2 x^{2} ight. $$ $$ =3 x^{2} imes 7 x^{2} 12 \quad 3 x^{2} imes 2 x^{2}-7 imes 12-7 imes 2 x^{2} $$ $$ =36 x^{2}+6 x^{4}-84-14 x^{2} $$ $$ =36 x^{2}-14 x^{2}+6 x^{4}-84 $$ $$ =22 x^{2}+6 x^{4}-84 $$ 3q) $$ (2 q-4 q)(4 p-2 q) \quad(2 q-4 q)(4 p-2 q) $$ $$ 2 q x^{4} p \quad 2 q imes-2 q-4 q imes 4 p $$

Question

3e) $$ (a-b)(3 a+7 b) \quad(1-b)(3 a+7 b) $$ $$ =a 	imes 3 a \quad a 	imes 7 b-b 	imes 3 a \quad-b 	imes 7 b $$ $$ =3 a^{2}+7 a b-3 a b-70 $$ $$ =3 a^{2}+4 a b-7 b $$ 3f) $$ \left(3 x^{2}-7ight)\left(12+2 x^{2}ight) \quad\left(35 x^{2}-7ight)\left(12+2 x^{2}ight. $$ $$ =3 x^{2} 	imes 7 x^{2} 12 \quad 3 x^{2} 	imes 2 x^{2}-7 	imes 12-7 	imes 2 x^{2} $$ $$ =36 x^{2}+6 x^{4}-84-14 x^{2} $$ $$ =36 x^{2}-14 x^{2}+6 x^{4}-84 $$ $$ =22 x^{2}+6 x^{4}-84 $$ 3q) $$ (2 q-4 q)(4 p-2 q) \quad(2 q-4 q)(4 p-2 q) $$ $$ 2 q x^{4} p \quad 2 q 	imes-2 q-4 q 	imes 4 p $$

UpStudy AI · Accepted Answer

**3e)**

Expand 
$$
(a-b)(3a+7b)
$$
Step 1: Distribute each term in the first parentheses:
$$
= a(3a+7b) - b(3a+7b)
$$

Step 2: Multiply each factor:
$$
= 3a^2+7ab - 3ab - 7b^2
$$

Step 3: Combine like terms:
$$
= 3a^2 + (7ab-3ab) - 7b^2 = 3a^2+4ab-7b^2
$$

For the expression 
$$
(1-b)(3a+7b),
$$
repeat a similar process.

Step 1: Distribute:
$$
= 1\cdot(3a+7b) - b(3a+7b)
$$

Step 2: Multiply:
$$
= 3a+7b - 3ab-7b^2
$$

---

**3f)**

Expand 
$$
(3x^2-7)(12+2x^2)
$$
Step 1: Distribute each term:
$$
= 3x^2\cdot12 + 3x^2\cdot2x^2 - 7\cdot12 - 7\cdot2x^2
$$

Step 2: Compute each product:
$$
= 36x^2 + 6x^4 - 84 - 14x^2
$$

Step 3: Combine like terms:
$$
= 6x^4 + (36x^2-14x^2) - 84 = 6x^4+22x^2-84
$$

---

**3q)**

Simplify 
$$
(2q-4q)(4p-2q)
$$
Step 1: Combine like terms in the first parentheses:
$$
2q-4q = -2q
$$
Thus the expression becomes:
$$
=-2q(4p-2q)
$$

Step 2: Distribute $$-2q$$:
$$
= -2q\cdot4p + (-2q)\cdot(-2q)
$$
$$
= -8pq + 4q^2
$$
  
Final Answer for 3q:
$$
-8pq+4q^2
$$
**3e)** $$ (a - b)(3a + 7b) = 3a^2 + 4ab - 7b^2 $$ $$ (1 - b)(3a + 7b) = 6a^2 + 22ab - 84 $$ **3f)** $$ (3x^2 - 7)(12 + 2x^2) = 6x^4 + 22x^2 - 84 $$ **3q)** $$ (2q - 4q)(4p - 2q) = -8pq + 4q^2 $$

3e)

3f)

3q)

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