6 This is part of Razi's homework. He has made a mistake in every question. Question Expand and simplify each expression. 1. \( 3(a+5)-5(3 a+5) \) 2. \( p(4 q+r)+q(2 r-4 p) \) 3. \( 5 b(b+3 a)+a(4 a+6 b) \) Answer 1. \( 3(a+5)-3(3 a+5)=3 a+15-9 a-15 \) \[ =6 a+30 \] 2. \( p(4 q+r)+q(2 r-4 p)=4 p q+p r+2 q r-4 p q \) \[ =3 p r+p q \] \[ =4 p^{2} q r \] 3. \( 5 b(b+3 a)+a(4 a+6 b)=5 b^{2}+15 a b+5 a b+4 a^{2}+6 a b \) \[ =4 a^{2}+5 b^{2}+11 a b \] a Explain what he has done wrong. b Work out the correct answers.

Oops! Razi has made several missteps in his calculations. In expression 1, he might have mistakenly multiplied terms incorrectly or mixed up signs when distributing. Additionally, he seems to have forgotten to simplify his expressions properly. In expressions 2 and 3, he's made errors both in the distribution and in combining terms—it's easy to lose track! Now, onto the proper solutions! For expression 1: \( 3(a+5)-5(3a+5) \) simplifies to: 1. \( 3a + 15 - 15a - 25 = -12a - 10 \). For expression 2: \( p(4q + r) + q(2r - 4p) \) simplifies to: 2. \( 4pq + pr + 2qr - 4pq = pr + 2qr \). For expression 3: \( 5b(b + 3a) + a(4a + 6b) \) simplifies to: 3. \( 5b^2 + 15ab + 4a^2 + 6ab = 5b^2 + 4a^2 + 21ab \). Let Razi know it's all part of the learning journey!