# Simplify (a-b)(2x^2+9)-(b-a)(7x-6)

(a-b)(2×2+9)-(b-a)(7x-6)
Simplify each term.
Expand (a-b)(2×2+9) using the FOIL Method.
Apply the distributive property.
a(2×2+9)-b(2×2+9)-(b-a)(7x-6)
Apply the distributive property.
a(2×2)+a⋅9-b(2×2+9)-(b-a)(7x-6)
Apply the distributive property.
a(2×2)+a⋅9-b(2×2)-b⋅9-(b-a)(7x-6)
a(2×2)+a⋅9-b(2×2)-b⋅9-(b-a)(7x-6)
Simplify each term.
Rewrite using the commutative property of multiplication.
2ax2+a⋅9-b(2×2)-b⋅9-(b-a)(7x-6)
Move 9 to the left of a.
2ax2+9⋅a-b(2×2)-b⋅9-(b-a)(7x-6)
Rewrite using the commutative property of multiplication.
2ax2+9a-1⋅2(bx2)-b⋅9-(b-a)(7x-6)
Multiply -1 by 2.
2ax2+9a-2(bx2)-b⋅9-(b-a)(7x-6)
Multiply 9 by -1.
2ax2+9a-2bx2-9b-(b-a)(7x-6)
2ax2+9a-2bx2-9b-(b-a)(7x-6)
Apply the distributive property.
2ax2+9a-2bx2-9b+(-b–a)(7x-6)
Multiply –a.
Multiply -1 by -1.
2ax2+9a-2bx2-9b+(-b+1a)(7x-6)
Multiply a by 1.
2ax2+9a-2bx2-9b+(-b+a)(7x-6)
2ax2+9a-2bx2-9b+(-b+a)(7x-6)
Expand (-b+a)(7x-6) using the FOIL Method.
Apply the distributive property.
2ax2+9a-2bx2-9b-b(7x-6)+a(7x-6)
Apply the distributive property.
2ax2+9a-2bx2-9b-b(7x)-b⋅-6+a(7x-6)
Apply the distributive property.
2ax2+9a-2bx2-9b-b(7x)-b⋅-6+a(7x)+a⋅-6
2ax2+9a-2bx2-9b-b(7x)-b⋅-6+a(7x)+a⋅-6
Simplify each term.
Rewrite using the commutative property of multiplication.
2ax2+9a-2bx2-9b-1⋅7(bx)-b⋅-6+a(7x)+a⋅-6
Multiply -1 by 7.
2ax2+9a-2bx2-9b-7(bx)-b⋅-6+a(7x)+a⋅-6
Multiply -6 by -1.
2ax2+9a-2bx2-9b-7bx+6b+a(7x)+a⋅-6
Rewrite using the commutative property of multiplication.
2ax2+9a-2bx2-9b-7bx+6b+7ax+a⋅-6
Move -6 to the left of a.
2ax2+9a-2bx2-9b-7bx+6b+7ax-6a
2ax2+9a-2bx2-9b-7bx+6b+7ax-6a
2ax2+9a-2bx2-9b-7bx+6b+7ax-6a
Subtract 6a from 9a.
2ax2+3a-2bx2-9b-7bx+6b+7ax
2ax2+3a-2bx2-3b-7bx+7ax
Reorder.
Move -3b.
2ax2+3a-2bx2-7bx+7ax-3b
Move 3a.
2ax2-2bx2-7bx+7ax+3a-3b
Move -7bx.
2ax2-2bx2+7ax-7bx+3a-3b
2ax2-2bx2+7ax-7bx+3a-3b
2ax2-2bx2+7ax-7bx+3a-3b
Simplify (a-b)(2x^2+9)-(b-a)(7x-6)