Apply the exponent rule b⁰ = 1.

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a) Step 1: Apply the exponent rule b⁰ = 1. 3ab⁰ × 2a²b = 3a(1) × 2a²b Step 2: Multiply the coefficients. 3 × 2 = 6; Step 3: Multiply the a terms using the rule a^m × aⁿ = a^(m+n). a × a² = a¹⁺² = a³ Step 4: Multiply the b terms. 1 × b = b Step 5: Combine the results. 6a³b The simplified expression is: 6a³b b) Step 1: Distribute −x to each term inside the parentheses. −x(2x+7) = (−x)(2x) + (−x)(7) Step 2: Perform the multiplications. −2x² − 7x The simplified expression is: −2x² − 7x c) Step 1: Distribute 3x² to each term inside the parentheses. 3x²(x²+2) = (3x²)(x²) + (3x²)(2); Step 2: Perform the multiplications using the rule x^m × xⁿ = x^(m+n). 3x²⁺² + 6x² 3x⁴ + 6x² The simplified expression is: 3x⁴ + 6x² d) Step 1: Distribute −5 to each term inside the parentheses. −5(2x−6y+4) = (−5)(2x) + (−5)(−6y) + (−5)(4) Step 2: Perform the multiplications. −10x + 30y − 20 The simplified expression is: −10x + 30y − 20 e) Step 1: Apply the exponent rule p⁰ = 1 inside the parentheses. 7p(−2p⁰+4p−1) = 7p(−2(1)+4p−1) 7p(−2+4p−1) Step 2: Distribute 7p to each term inside the parentheses. 7p(−2) + 7p(4p) + 7p(−1) Step 3: Perform the multiplications. −14p + 28p² − 7p Step 4: Combine like terms. 28p² + (−14p − 7p) 28p² − 21p The simplified expression is: 28p² − 21p f) Step 1: Distribute 4y to each term inside the parentheses. 4y(2y−3x+6) = (4y)(2y) + (4y)(−3x) + (4y)(6) Step 2: Perform the multiplications. 8y² − 12xy + 24y The simplified expression is: 8y² − 12xy + 24y g) Step 1: Distribute 3m into the first set of parentheses. 3m(−4m−3n) = (3m)(−4m) + (3m)(−3n) −12m² − 9mn Step 2: Distribute −2m into the second set of parentheses. −2m(−b+n) = (−2m)(−b) + (−2m)(n) 2mb − 2mn Step 3: Combine the results from Step 1 and Step 2. (−12m² − 9mn) − (2mb − 2mn) Step 4: Distribute the negative sign to the terms in the second parenthesis. −12m² − 9mn − 2mb + 2mn Step 5: Combine like terms (−9mn and 2mn). −12m² + (−9mn + 2mn) − 2mb −12m² − 7mn − 2mb The simplified expression is: −12m² − 7mn − 2mb h) Step 1: Distribute 4x into the first set of parentheses. 4x(x+2) = (4x)(x) + (4x)(2) 4x² + 8x Step 2: Distribute −3x into the second set of parentheses. −3x(x−4) = (−3x)(x) + (−3x)(−4) −3x² + 12x Step 3: Combine the results from Step 1 and Step 2. (4x² + 8x) + (−3x² + 12x) Step 4: Remove the parentheses. 4x² + 8x − 3x² + 12x Step 5: Combine like terms (4x² with −3x², and 8x with 12x). (4x² − 3x²) + (8x + 12x) x² + 20x The simplified expression is: x² + 20x

Apply the exponent rule b⁰ = 1.

Answers

Step-by-step solution

Part a· 5 steps

Apply the exponent rule b0=1b^0 = 1b0=1.

Multiply the coefficients.

Multiply the aaa terms using the rule am×an=am+na^m \times a^n = a^{m+n}am×an=am+n.

Multiply the bbb terms.

Combine the results.

Part b· 2 steps−2x2−7x-2x^2 - 7x−2x2−7x

Distribute −x-x−x to each term inside the parentheses.

Perform the multiplications.

Part c· 2 steps3x4+6x23x^4 + 6x^23x4+6x2

Distribute 3x23x^23x2 to each term inside the parentheses.

Perform the multiplications using the rule xm×xn=xm+nx^m \times x^n = x^{m+n}xm×xn=xm+n.

Part d· 2 steps-10x + 30y - 20

Distribute −5-5−5 to each term inside the parentheses.

Perform the multiplications.

Part e· 4 steps28p2−21p28p^2 - 21p28p2−21p

Apply the exponent rule p0=1p^0 = 1p0=1 inside the parentheses.

Distribute $7p$ to each term inside the parentheses.

Perform the multiplications.

Combine like terms.

Part f· 2 steps8y2−12xy+24y8y^2 - 12xy + 24y8y2−12xy+24y

Distribute $4y$ to each term inside the parentheses.

Perform the multiplications.

Part g· 5 steps−12m2−7mn−2mb-12m^2 - 7mn - 2mb−12m2−7mn−2mb

Distribute $3m$ into the first set of parentheses.

Distribute −2m-2m−2m into the second set of parentheses.

Combine the results from Step 1 and Step 2.

Distribute the negative sign to the terms in the second parenthesis.

Combine like terms (−9mn-9mn−9mn and 2mn2mn2mn).

Part h· 5 stepsx2+20xx^2 + 20xx2+20x

Distribute $4x$ into the first set of parentheses.

Distribute −3x-3x−3x into the second set of parentheses.

Combine the results from Step 1 and Step 2.

Remove the parentheses.

Combine like terms (4x24x^24x2 with −3x2-3x^2−3x2, and 8x8x8x with 12x12x12x).

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More Mathematics Questions

Apply the exponent rule $b^0 = 1$ .

Multiply the $a$ terms using the rule $a^m \times a^n = a^{m+n}$ .

Multiply the $b$ terms.

Part b· 2 steps
$-2x^2 - 7x$

Distribute $-x$ to each term inside the parentheses.

Part c· 2 steps
$3x^4 + 6x^2$

Distribute $3x^2$ to each term inside the parentheses.

Perform the multiplications using the rule $x^m \times x^n = x^{m+n}$ .

Distribute $-5$ to each term inside the parentheses.

Part e· 4 steps
$28p^2 - 21p$

Apply the exponent rule $p^0 = 1$ inside the parentheses.

Part f· 2 steps
$8y^2 - 12xy + 24y$

Part g· 5 steps
$-12m^2 - 7mn - 2mb$

Distribute $-2m$ into the second set of parentheses.

Combine like terms ( $-9mn$ and $2mn$ ).

Part h· 5 steps
$x^2 + 20x$

Distribute $-3x$ into the second set of parentheses.

Combine like terms ( $4x^2$ with $-3x^2$ , and $8x$ with $12x$ ).