1. Problem: Simplify the expression $11(3g + 7 - 2g) - 4$. 2. Use the distributive property: $a(b + c) = ab + ac$. 3. Distribute 11: $$11 \times 3g + 11 \times 7 - 11 \times 2g - 4 = 33g + 77 - 22g - 4$$ 4. Combine like terms: $$33g - 22g + 77 - 4 = (33 - 22)g + (77 - 4) = 11g + 73$$ --- 1. Problem: Simplify $-2(d^6 + 11) - d(14 + d^5)$. 2. Distribute: $$-2d^6 - 22 - 14d - d^{6} = -2d^6 - 22 - 14d - d^6$$ 3. Combine like terms: $$-2d^6 - d^6 - 14d - 22 = (-2 - 1)d^6 - 14d - 22 = -3d^6 - 14d - 22$$ --- 1. Problem: Simplify $2a^2 - 8a^2 + 5a^3 - 11a^2$. 2. Combine like terms for $a^2$: $$2a^2 - 8a^2 - 11a^2 = (2 - 8 - 11)a^2 = -17a^2$$ 3. Expression becomes: $$5a^3 - 17a^2$$ --- 1. Problem: Simplify $10x^3 - 2x^2 + 5x^3 - 6x^2$. 2. Combine like terms for $x^3$: $$10x^3 + 5x^3 = 15x^3$$ 3. Combine like terms for $x^2$: $$-2x^2 - 6x^2 = -8x^2$$ 4. Expression becomes: $$15x^3 - 8x^2$$ --- 1. Problem: Simplify $6(b^2 - 2b^4 + 5) - 10b^4 - 9b^2$. 2. Distribute 6: $$6b^2 - 12b^4 + 30 - 10b^4 - 9b^2$$ 3. Combine like terms for $b^4$: $$-12b^4 - 10b^4 = -22b^4$$ 4. Combine like terms for $b^2$: $$6b^2 - 9b^2 = -3b^2$$ 5. Expression becomes: $$-22b^4 - 3b^2 + 30$$ --- 1. Problem: Simplify $-20 + 5(7t - 2)$. 2. Distribute 5: $$-20 + 35t - 10$$ 3. Combine constants: $$-20 - 10 = -30$$ 4. Expression becomes: $$35t - 30$$ --- 1. Problem: Simplify $4(9 + 4k) - 2(2k - 3)$. 2. Distribute: $$36 + 16k - 4k + 6$$ 3. Combine like terms for $k$: $$16k - 4k = 12k$$ 4. Combine constants: $$36 + 6 = 42$$ 5. Expression becomes: $$12k + 42$$ --- 1. Problem: Simplify $7y + y - 5y + 12 - 5 + 6$. 2. Combine like terms for $y$: $$7y + y - 5y = (7 + 1 - 5)y = 3y$$ 3. Combine constants: $$12 - 5 + 6 = 13$$ 4. Expression becomes: $$3y + 13$$ --- 1. Problem: Simplify $-32 - 8a + 12 - 2a - 4$. 2. Combine like terms for $a$: $$-8a - 2a = -10a$$ 3. Combine constants: $$-32 + 12 - 4 = -24$$ 4. Expression becomes: $$-10a - 24$$ --- 1. Problem: Simplify $10a - 2(11 + 6a - 3)$. 2. Simplify inside parentheses: $$11 - 3 = 8$$ 3. Expression becomes: $$10a - 2(8 + 6a)$$ 4. Distribute $-2$: $$10a - 16 - 12a$$ 5. Combine like terms for $a$: $$10a - 12a = -2a$$ 6. Final expression: $$-2a - 16$$