Simplify the following expressions using the FOIL method: a) (p+3)(p+5) b) (k+7)(k−2) c) (c−4)(c−8) d)…

Question

Simplify the following expressions using the FOIL method: a) (p+3)(p+5) b) (k+7)(k−2) c) (c−4)(c−8) d) (f+5)(f−5) e) (m−8)(m+7)

ScanSolve AI Tutor · Accepted Answer

let's simplify these expressions, kamogelo. a) Simplify (p+3)(p+5). Step 1: Use the FOIL method (First, Outer, Inner, Last) to multiply the binomials. (p+3)(p+5) = p · p + p · 5 + 3 · p + 3 · 5 Step 2: Perform the multiplications. p² + 5p + 3p + 15 Step 3: Combine like terms. p² + 8p + 15 The simplified expression is p² + 8p + 15. b) Simplify (k+7)(k−2). Step 1: Use the FOIL method to multiply the binomials. (k+7)(k−2) = k · k + k · (−2) + 7 · k + 7 · (−2) Step 2: Perform the multiplications. k² − 2k + 7k − 14 Step 3: Combine like terms. k² + 5k − 14 The simplified expression is k² + 5k − 14. c) Simplify (c−4)(c−8). Step 1: Use the FOIL method to multiply the binomials. (c−4)(c−8) = c · c + c · (−8) + (−4) · c + (−4) · (−8) Step 2: Perform the multiplications. c² − 8c − 4c + 32 Step 3: Combine like terms. c² − 12c + 32 The simplified expression is c² − 12c + 32. d) Simplify (f+5)(f−5). Step 1: Recognize this as a difference of squares pattern, (A+B)(A−B) = A² − B². (f+5)(f−5) = f² − 5² Step 2: Calculate the square. f² − 25 The simplified expression is f² − 25. e) Simplify (m−8)(m+7). Step 1: Use the FOIL method to multiply the binomials. (m−8)(m+7) = m · m + m · 7 + (−8) · m + (−8) · 7 Step 2: Perform the multiplications. m² + 7m − 8m − 56 Step 3: Combine like terms. m² − m − 56 The simplified expression is m² − m − 56. f) Simplify (r+6)². Step 1: Use the square of a binomial formula, (A+B)² = A² + 2AB + B². (r+6)² = r² + 2(r)(6) + 6² Step 2: Perform the multiplications and squaring. r² + 12r + 36 The simplified expression is r² + 12r + 36. g) Simplify (r−3)². Step 1: Use the square of a binomial formula, (A−B)² = A² − 2AB + B². (r−3)² = r² − 2(r)(3) + 3² Step 2: Perform the multiplications and squaring. r² − 6r + 9 The simplified expression is r² − 6r + 9. h) Simplify (m−7)². Step 1: Use the square of a binomial formula, (A−B)² = A² − 2AB + B². (m−7)² = m² − 2(m)(7) + 7² Step 2: Perform the multiplications and squaring. m² − 14m + 49 The simplified expression is m² − 14m + 49. i) Simplify 7m(7m²−4n). Step 1: Distribute 7m to each term inside the parenthesis. 7m(7m²−4n) = (7m)(7m²) − (7m)(4n) Step 2: Perform the multiplications. 49m³ − 28mn The simplified expression is 49m³ − 28mn. j) Simplify 1/2(8x²+6)(3x³). Step 1: Multiply the terms inside the first parenthesis by 3x³. 1/2 [ (8x²)(3x³) + (6)(3x³) ] Step 2: Perform the multiplications inside the bracket. 1/2 [ 24x²⁺³ + 18x³ ] 1/2 [ 24x⁵ + 18x³ ] Step 3: Distribute 1/2 to each term inside the bracket. 1/2(24x⁵) + 1/2(18x³) 12x⁵ + 9x³ The simplified expression is 12x⁵ + 9x³.

Simplify the following expressions using the FOIL method: a) (p+3)(p+5) b) (k+7)(k-2) c) (c-4)(c-8) d) (f+5)(f-5) e) (m-8)(m+7)

Step-by-step solution

Part a· 3 steps

Use the FOIL method (First, Outer, Inner, Last) to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part b· 3 steps

Use the FOIL method to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part c· 3 steps

Use the FOIL method to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part d· 2 steps

Recognize this as a difference of squares pattern, $(A+B)(A-B) = A^2 - B^2$ .

Calculate the square.

Part e· 3 steps

Use the FOIL method to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part f· 2 steps

Use the square of a binomial formula, $(A+B)^2 = A^2 + 2AB + B^2$ .

Perform the multiplications and squaring.

Part g· 2 steps

Use the square of a binomial formula, $(A-B)^2 = A^2 - 2AB + B^2$ .

Perform the multiplications and squaring.

Part h· 2 steps

Use the square of a binomial formula, $(A-B)^2 = A^2 - 2AB + B^2$ .

Perform the multiplications and squaring.

Part h(i)· 5 steps

Distribute $7m$ to each term inside the parenthesis.

Perform the multiplications.

Multiply the terms inside the first parenthesis by $3x^3$ .

Perform the multiplications inside the bracket.

Distribute $\frac{1}{2}$ to each term inside the bracket.

Still stuck on this one?

More Mathematics Questions

Simplify the following expressions using the FOIL method: a) (p+3)(p+5) b) (k+7)(k-2) c) (c-4)(c-8) d) (f+5)(f-5) e) (m-8)(m+7)

Step-by-step solution

Part a· 3 steps

Use the FOIL method (First, Outer, Inner, Last) to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part b· 3 steps

Use the FOIL method to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part c· 3 steps

Use the FOIL method to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part d· 2 steps

Recognize this as a difference of squares pattern, (A+B)(A−B)=A2−B2(A+B)(A-B) = A^2 - B^2(A+B)(A−B)=A2−B2.

Calculate the square.

Part e· 3 steps

Use the FOIL method to multiply the binomials.

Perform the multiplications.

Combine like terms.

Part f· 2 steps

Use the square of a binomial formula, (A+B)2=A2+2AB+B2(A+B)^2 = A^2 + 2AB + B^2(A+B)2=A2+2AB+B2.

Perform the multiplications and squaring.

Part g· 2 steps

Use the square of a binomial formula, (A−B)2=A2−2AB+B2(A-B)^2 = A^2 - 2AB + B^2(A−B)2=A2−2AB+B2.

Perform the multiplications and squaring.

Part h· 2 steps

Use the square of a binomial formula, (A−B)2=A2−2AB+B2(A-B)^2 = A^2 - 2AB + B^2(A−B)2=A2−2AB+B2.

Perform the multiplications and squaring.

Part h(i)· 5 steps

Distribute $7m$ to each term inside the parenthesis.

Perform the multiplications.

Multiply the terms inside the first parenthesis by 3x33x^33x3.

Perform the multiplications inside the bracket.

Distribute 12\frac{1}{2}21​ to each term inside the bracket.

Still stuck on this one?

More Mathematics Questions

Recognize this as a difference of squares pattern, $(A+B)(A-B) = A^2 - B^2$ .

Use the square of a binomial formula, $(A+B)^2 = A^2 + 2AB + B^2$ .

Use the square of a binomial formula, $(A-B)^2 = A^2 - 2AB + B^2$ .

Use the square of a binomial formula, $(A-B)^2 = A^2 - 2AB + B^2$ .

Multiply the terms inside the first parenthesis by $3x^3$ .

Distribute $\frac{1}{2}$ to each term inside the bracket.