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problems with polynomials
1.expand 3(5× - 12)
2.factorize 15a² + 30a
3.Expand and collect like terms to simplify 5(3t - 4) + 6( 4 - 5t)
4.factorize x² + 9× + 20
5.expand (x - 3)²​


Sagot :

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