1Expand $$(3x−5)(4x−7)$$.
$$(3x−5)(4x−7) \\ \, \\ =\underbrace{(3x\cdot 4x)}_{\text{First Terms}}+\underbrace{(3x\cdot-7)}_{\text{Outer Terms}}+\underbrace{(-5\cdot 4x)}_{\text{Inner Terms}}+\underbrace{(-5\cdot-7)}_{\text{Last Terms}} \\ \, \\ =12x^2-21x-20x+35 \\ =12x^2-41x+35$$

2Expand $$(2p-q)(3+4q)$$.
$$(2p-q)(3+4q) \\ \, \\ =\underbrace{(2p\cdot 3)}_{\text{First Terms}}+\underbrace{(2p\cdot4q)}_{\text{Outer Terms}}+\underbrace{(-q\cdot 3)}_{\text{Inner Terms}}+\underbrace{(-q\cdot4q)}_{\text{Last Terms}} \\ \, \\ =6p+8pq-3q-4q^2$$

3Expand $$(y+2x)(x+2y)$$.
$$(y+2x)(x+2y) \\ \, \\ =\underbrace{(y\cdot x)}_{\text{First Terms}}+\underbrace{(y\cdot2y)}_{\text{Outer Terms}}+\underbrace{(2x\cdot x)}_{\text{Inner Terms}}+\underbrace{(2x\cdot2y)}_{\text{Last Terms}} \\ \, \\ =xy+2y^2+2x^2+4xy \\ =2y^2+2x^2+(xy+4xy) \\ =2y^2+2x^2+5xy$$

4Expand $$(5a+b)(6-2a)$$.
$$(5a+b)(6-2a) \\ \, \\ =\underbrace{(5a\cdot 6)}_{\text{First Terms}}+\underbrace{(5a\cdot-2a)}_{\text{Outer Terms}}+\underbrace{(b\cdot 6)}_{\text{Inner Terms}}+\underbrace{(b\cdot-2a)}_{\text{Last Terms}} \\ \, \\ =30a-10a^2+6b-2ab$$

5Expand $$(3k+7)(3k−7)$$.
$$(3k+7)(3k−7) \\ \, \\ =\underbrace{(3k)^2}_{A^2}-\underbrace{(7)^2}_{B^2} \\ \, \\ =9k^2-49$$

Note: This is Type 3, $$(A+B)(A-B)=A^2-B^2$$

6Expand $$(4xy+9)(4xy−9)$$.
$$(4xy+9)(4xy−9) \\ =\underbrace{(4xy)^2}_{A^2}-\underbrace{(9)^2}_{B^2} \\ =16x^2y^2-81$$

Note: This is Type 3, $$(A+B)(A-B)=A^2-B^2$$

7Expand $$(7ab-b)^2$$.
$$(7ab-b)^2 \\ \, \\ =\underbrace{(7ab)^2}_{A^2}-\underbrace{2(7ab)(b)}_{2AB}+\underbrace{(b)^2}_{B^2} \\ \, \\ =49a^2b^2-14ab^2+b^2$$

Note: This is Type 2, $$(A – B)^2=A^2-2AB+B^2$$

8Expand $$(6+9y)^2$$.
$$(6+9y)^2 \\ \, \\ =\underbrace{(6)^2}_{A^2}+\underbrace{2(6)(9y)}_{2AB}+\underbrace{(9y)^2}_{B^2} \\ \, \\ =36+108y+81y^2$$

Note: This is Type 1, $$(A + B)^2=A^2+2AB+B^2$$

9Expand $$(2p+5)(2p+5)$$.
$$(2p+5)(2p+5) \\ \, \\ =(2p+5)^2 \\ =\underbrace{(2p)^2}_{A^2}+\underbrace{2(2p)(5)}_{2AB}+\underbrace{(5)^2}_{B^2} \\ \, \\ =4p^2+20p+25$$
Note: This is Type 1, $$(A + B)^2=A^2+2AB+B^2$$
10 Expand $$(3k-6km)^2$$.
$$(3k-6km)^2 \\ \, \\ =\underbrace{(3k)^2}_{A^2}-\underbrace{2(3k)(6km)}_{2AB}+\underbrace{(6km)^2}_{B^2} \\ \, \\ =9k^2-36k^2m+36k^2m^2$$
Note: This is Type 2, $$(A – B)^2=A^2-2AB+B^2$$