Question

name ______________ algebra i 1.06a - simplify expressions with distribution (day 1) directions: simplify each of the expressions below. 1. 5(3x - 5) 2. 4(p + 4) + 3(p - 1) 3. 2(x - 4) + 4 - 2(x + 2) - 1 4. 3(x² - y) + 9(x² + 2y) 5. * -4(x - 1 + 4y) - 3x + 2

Explanation:

Step1: Distribute 5 in 5(3x - 5)

$5\times3x-5\times5 = 15x - 25$

Step2: Distribute in 4(p + 4)+3(p - 1)

$4p+16 + 3p-3$

Step3: Combine like - terms in 4p+16 + 3p-3

$(4p + 3p)+(16 - 3)=7p + 13$

Step4: Distribute in 2(x - 4)+4-2(x + 2)-1

$2x-8 + 4-2x-4-1$

Step5: Combine like - terms in 2x-8 + 4-2x-4-1

$(2x-2x)+(-8 + 4-4-1)=-9$

Step6: Distribute in 3(x² - y)+9(x² + 2y)

$3x²-3y+9x² + 18y$

Step7: Combine like - terms in 3x²-3y+9x² + 18y

$(3x²+9x²)+(-3y + 18y)=12x²+15y$

Step8: Distribute in -4(x - 1 + 4y)-3x + 2

$-4x+4-16y-3x + 2$

Step9: Combine like - terms in -4x+4-16y-3x + 2

$(-4x-3x)-16y+(4 + 2)=-7x-16y + 6$

Answer:

1. $15x - 25$
2. $7p + 13$
3. $-9$
4. $12x²+15y$
5. $-7x-16y + 6$