Solve (k+4y)^2-4(2-y)(10-6y)

$$( k + 4 y ) ^ { 2 } - 4 ( 2 - y ) ( 10 - 6 y )$$

Evaluate

$$\left(4y+k\right)^{2}-24y^{2}+88y-80$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(k+4y\right)^{2}.

$$k^{2}+8ky+16y^{2}-4\left(2-y\right)\left(10-6y\right)$$

Use the distributive property to multiply -4 by 2-y.

$$k^{2}+8ky+16y^{2}+\left(-8+4y\right)\left(10-6y\right)$$

Use the distributive property to multiply -8+4y by 10-6y and combine like terms.

$$k^{2}+8ky+16y^{2}-80+88y-24y^{2}$$

Combine 16y^{2} and -24y^{2} to get -8y^{2}.

$$k^{2}+8ky-8y^{2}-80+88y$$

Expand

$$-8y^{2}+8ky+88y+k^{2}-80$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(k+4y\right)^{2}.

$$k^{2}+8ky+16y^{2}-4\left(2-y\right)\left(10-6y\right)$$

Use the distributive property to multiply -4 by 2-y.

$$k^{2}+8ky+16y^{2}+\left(-8+4y\right)\left(10-6y\right)$$

Use the distributive property to multiply -8+4y by 10-6y and combine like terms.

$$k^{2}+8ky+16y^{2}-80+88y-24y^{2}$$

Combine 16y^{2} and -24y^{2} to get -8y^{2}.

$$k^{2}+8ky-8y^{2}-80+88y$$