Solve 4-28(y-3)+49(y-3)^2

$$4 - 28 ( y - 3 ) + 49 ( y - 3 ) ^ { 2 }$$

Evaluate

$$\left(7y-23\right)^{2}$$

Solution Steps

Use the distributive property to multiply -28 by y-3.

$$4-28y+84+49\left(y-3\right)^{2}$$

Add 4 and 84 to get 88.

$$88-28y+49\left(y-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.

$$88-28y+49\left(y^{2}-6y+9\right)$$

Use the distributive property to multiply 49 by y^{2}-6y+9.

$$88-28y+49y^{2}-294y+441$$

Combine -28y and -294y to get -322y.

$$88-322y+49y^{2}+441$$

Add 88 and 441 to get 529.

$$529-322y+49y^{2}$$

Expand

$$49y^{2}-322y+529$$

Solution Steps

Use the distributive property to multiply -28 by y-3.

$$4-28y+84+49\left(y-3\right)^{2}$$

Add 4 and 84 to get 88.

$$88-28y+49\left(y-3\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-3\right)^{2}.

$$88-28y+49\left(y^{2}-6y+9\right)$$

Use the distributive property to multiply 49 by y^{2}-6y+9.

$$88-28y+49y^{2}-294y+441$$

Combine -28y and -294y to get -322y.

$$88-322y+49y^{2}+441$$

Add 88 and 441 to get 529.

$$529-322y+49y^{2}$$