Simplify each expression. Write answers in standard form.
a. (4d-6)(-3d)
b. 5g(g^2-2g+1)
c. (-2q^2+q+3)-5(q^2+2q-1)
a )
( 4 d - 6 )( - 3 d ) =
4 d * ( - 3 d ) - 6 * ( - 3 d ) =
- 12 d ^ 2 + 18 d
b )
5 g ( g ^ 2 - 2 g + 1 ) =
5 g * g ^ 2 - 5 g * 2 g + 5 g * 1 =
5 g ^ 3 - 10 g ^ 2 + 5 g
c )
( - 2 q ^ 2 + q + 3 ) - 5 ( q ^ 2 + 2 q - 1 ) =
- 2 q ^ 2 + q + 3 - 5 q ^ 2 - 10 q + 5 =
- 2 q ^ 2 - 5 q ^ 2 + q - 10 q + 3 + 5
- 7 q ^ 2 - 9 q + 8
( - 2 q ^ 2 + q + 3 ) - 5 ( q ^ 2 + 2 q - 1 ) = - 7 q ^ 2 - 9 q + 8
To simplify each expression and write the answers in standard form, we'll follow these steps:
a. (4d-6)(-3d)
1. Multiply the terms inside the parentheses: 4d * -3d = -12d^2
2. Multiply the last terms: -6 * -3d = 18d
3. Combine the results from step 1 and step 2: -12d^2 + 18d
So, the simplified expression in standard form is -12d^2 + 18d.
b. 5g(g^2-2g+1)
1. Multiply the terms inside the parentheses: g^2 * 5g = 5g^3, -2g * 5g = -10g^2, 1 * 5g = 5g
2. Combine the results from step 1: 5g^3 - 10g^2 + 5g
So, the simplified expression in standard form is 5g^3 - 10g^2 + 5g.
c. (-2q^2+q+3)-5(q^2+2q-1)
1. Multiply the terms inside the second set of parentheses: q^2 * -5 = -5q^2, 2q * -5 = -10q, -1 * -5 = 5
2. Distribute the -5 to each term inside the second set of parentheses: -5q^2 - 10q + 5
3. Combine like terms: (-2q^2 + q + 3) -5q^2 - 10q + 5 = -2q^2 - 5q^2 + q - 10q + 3 + 5
4. Combine similar terms: (-2q^2 - 5q^2) + (q - 10q) + (3 + 5) = -7q^2 - 9q + 8
So, the simplified expression in standard form is -7q^2 - 9q + 8.