Distribute 7 to binomial: Distribute the 7 to the binomial (2y+z). 7(2y+z) = 7*2y + 7*z = 14y + 7zMultiply binomials using FOIL: Now we have to multiply the result from Step 1 with the second binomial (9y-4z). (14y + 7z)(9y - 4z) We will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first binomial by each term in the second binomial.Multiply first term with second binomial: Multiply the first term of the first binomial by each term of the second binomial. 14y * 9y = 126y^2 14y * (-4z) = -56yzMultiply second term with second binomial: Multiply the second term of the first binomial by each term of the second binomial. 7z * 9y = 63yz 7z * (-4z) = -28z^2Combine results: Combine the results from Step 3 and Step 4. 126y^2 - 56yz + 63yz - 28z^2Combine like terms: Combine like terms. 126y^2 + (63yz - 56yz) - 28z^2 126y^2 + 7yz - 28z^2

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

7(2y+z)(9y-4z)

Distribute $7$ to binomial: Distribute the $7$ to the binomial $(2y+z)$ . $7(2y+z) = 7\cdot 2y + 7\cdot z$ $= 14y + 7z$
Multiply binomials using FOIL: Now we have to multiply the result from Step $1$ with the second binomial $(9y-4z)$ . $(14y + 7z)(9y - 4z)$ We will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first binomial by each term in the second binomial.
Multiply first term with second binomial: Multiply the first term of the first binomial by each term of the second binomial. $\newline$ $14y \times 9y = 126y^2$ $\newline$ $14y \times (-4z) = -56yz$
Multiply second term with second binomial: Multiply the second term of the first binomial by each term of the second binomial. $\newline$ $7z \times 9y = 63yz$ $\newline$ $7z \times (-4z) = -28z^2$
Combine results: Combine the results from Step $3$ and Step $4$ . $126y^2 - 56yz + 63yz - 28z^2$
Combine like terms: Combine like terms. $\newline$ $126y^2 + (63yz - 56yz) - 28z^2$ $\newline$ $126y^2 + 7yz - 28z^2$