5 Expand and simplify each expression. a $$ a(a+3)+a(a+4) $$ b $$ b(b+3)+b(4 b+5) $$ c $$ c(3 c+4)+c(5 c+6) $$ d $$ d(3 d+4)-d(d+5) $$ e $$ e(3+4 e)-e(5 e-6) $$ f $$ f(3 f+4 g)-5 f(6 f-7 g) $$

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**a)**  
$$
a(a+3)+a(a+4)=a\Big[(a+3)+(a+4)\Big]
$$
$$
= a(2a+7)
$$
$$
= 2a^2+7a
$$

**b)**  
$$
b(b+3)+b(4b+5)=b\Big[(b+3)+(4b+5)\Big]
$$
$$
= b(5b+8)
$$
$$
= 5b^2+8b
$$

**c)**  
$$
c(3c+4)+c(5c+6)=c\Big[(3c+4)+(5c+6)\Big]
$$
$$
= c(8c+10)
$$
$$
= 8c^2+10c
$$

**d)**  
$$
d(3d+4)-d(d+5)=d\Big[(3d+4)-(d+5)\Big]
$$
$$
= d\big(3d+4-d-5\big)
$$
$$
= d(2d-1)
$$
$$
= 2d^2-d
$$

**e)**  
$$
e(3+4e)-e(5e-6)=e\Big[(3+4e)-(5e-6)\Big]
$$
$$
= e\big(3+4e-5e+6\big)
$$
$$
= e(9-e)
$$
$$
= 9e-e^2
$$

**f)**  
$$
f(3f+4g)-5f(6f-7g)=f\Big[(3f+4g)-5(6f-7g)\Big]
$$
$$
= f\big[3f+4g-30f+35g\big]
$$
$$
= f(-27f+39g)
$$
$$
= -27f^2+39fg
$$
a) $$ 2a^2 + 7a $$ b) $$ 5b^2 + 8b $$ c) $$ 8c^2 + 10c $$ d) $$ 2d^2 - d $$ e) $$ 9e - e^2 $$ f) $$ -27f^2 + 39fg $$

5 Expand and simplify each expression. a \( a(a+3)+a(a+4) \) b \( b(b+3)+b(4 b+5) \) c \( c(3 c+4)+c(5 c+6) \) d \( d(3 d+4)-d(d+5) \) e \( e(3+4 e)-e(5 e-6) \) f \( f(3 f+4 g)-5 f(6 f-7 g) \)

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