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Answer:
1. Expand 3(5x - 12)3(5x−12)
3(5x - 12) = 3 \cdot 5x - 3 \cdot 12 = 15x - 363(5x−12)=3⋅5x−3⋅12=15x−36
2. Factorize 15a^2 + 30a15a
2
+30a
15a^2 + 30a = 15a(a + 2)15a
2
+30a=15a(a+2)
3. Expand and collect like terms to simplify 5(3t - 4) + 6(4 - 5t)5(3t−4)+6(4−5t)
5(3t - 4) + 6(4 - 5t) = 15t - 20 + 24 - 30t5(3t−4)+6(4−5t)=15t−20+24−30t
= 15t - 30t - 20 + 24=15t−30t−20+24
= -15t + 4=−15t+4
4. Factorize x^2 + 9x + 20x
2
+9x+20
To factorize x^2 + 9x + 20x
2
+9x+20, we need two numbers that multiply to 20 and add up to 9. These numbers are 4 and 5.
x^2 + 9x + 20 = (x + 4)(x + 5)x
2
+9x+20=(x+4)(x+5)
5. Expand (x - 3)^2(x−3)
2
(x - 3)^2 = (x - 3)(x - 3)(x−3)
2
=(x−3)(x−3)
= x(x - 3) - 3(x - 3)=x(x−3)−3(x−3)
= x^2 - 3x - 3x + 9=x
2
−3x−3x+9
= x^2 - 6x + 9=x
2
−6x+9