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

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

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

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

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

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

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

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

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

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

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

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

9Expand \((2p+5)(2p+5)\).
Answer
\((2p+5)(2p+5) \\ \, \\ =(2p+5)^2 \\ =\underbrace{(2p)^2}_{A^2}+\underbrace{2(2p)(5)}_{2AB}+\underbrace{(5)^2}_{B^2} \\ \, \\ =4p^2+20p+25\)

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

10 Expand \((3k-6km)^2\).
Answer
\((3k-6km)^2 \\ \, \\ =\underbrace{(3k)^2}_{A^2}-\underbrace{2(3k)(6km)}_{2AB}+\underbrace{(6km)^2}_{B^2} \\ \, \\ =9k^2-36k^2m+36k^2m^2\)

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

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